I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_011_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_012_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_013_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_014_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_016_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_017_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_018_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_019_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_020_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_021_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_022_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_024_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_025_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_026_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_027_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_028_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_029_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_030_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0352_031_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_000_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_001_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_002_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_003_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_005_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_006_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_007_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_008_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_009_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_010_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_011_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_014_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_015_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_018_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 315 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_019_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_024_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_025_z_45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>315</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_026_z_-45</image_path>


I'm showing you multiple images of 3D objects. For each example or test case, two images represent the same object before and after rotation.

Your task is to determine the angle of rotation around the z-axis in degrees.

The 3D Cartesian coordinate system is defined as follows:
- x-axis: points horizontally from left to right (positive direction is right)
- y-axis: points vertically from bottom to top (positive direction is up)
- z-axis: points from inside the image toward the viewer (positive direction is out of the screen)
- The origin (0,0,0) is located at the geometric center of the 3D object mesh

When discussing rotations around an axis, imagine looking along the positive direction of that axis (as if looking from the origin toward the positive end).

The rotation angle is one of these specific values: [45, 315] degrees. A positive angle means rotation in the CLOCKWISE direction when looking along the positive direction of the axis.

### EXAMPLE OF ROTATION ###

Example: Image 1 shows the initial view and Image 2 shows the object after a 45 degree rotation around the z-axis.

### YOUR TASK ###
Now, determine the angle of rotation around the z-axis from Image 3 to Image 4.
Based on the examples provided, analyze the rotation carefully.

IMPORTANT: Please follow this systematic approach to determine the rotation angle:

1. First, analyze the object's features in both views to understand its structure.

2. For the z-axis rotation, you must evaluate ONLY these possible rotation angles: [45, 315]
   - For each angle in the list, describe what the object would look like after rotating around the z-axis by that amount
   - Compare these descriptions with the actual second view
   - DO NOT make a decision until you have evaluated all possible angles in the list

3. After evaluating all angles, choose the one that best matches the observed changes

4. Verify your answer by mentally applying the rotation to confirm it matches the second view

Place your detailed reasoning process in <think></think> tags. Your reasoning should include:
- Systematic evaluation of possible rotation angles from the provided list
- Specific visual features you used to determine your answer

Then provide your final answer in <rotation_angle></rotation_angle> tags (use only a number from the list for angle).
i.e., <think> your reasoning process here </think><rotation_angle> your predicted degrees here </rotation_angle>

Answer: <angle>45</angle><image_path>/lustre/fsw/portfolios/av/users/shiyil/yunfei/MM-EUREKA/data/hunyuan_z_13k_clean/fig0353_027_z_45</image_path>