You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
Maggie Waggie organizes a pile of 127 calculus tests in alphabetical order, with Joccy Woccy's test being 64th in the pile. While Maggie isn't looking, Joccy walks over and randomly scrambles the entire pile of tests. When Maggie returns, she is oblivious to the fact that Joccy has tampered with the list. She uses a binary search algorithm to find Joccy's test, where she looks at the test in the middle of the pile. If the test is not Joccy's, she binary searches the top half of the list if the test appears after Joccy's name when arranged alphabetically, or the bottom half of the list otherwise. The probability that Maggie finds Joccy's test can be expressed as $\frac{p}{q}$. Compute $p+q$.
user
134
rule
Maggie Waggie organizes a pile of 127 calculus tests in alphabetical order, with Joccy Woccy's test being 64th in the pile. While Maggie isn't looking, Joccy walks over and randomly scrambles the entire pile of tests. When Maggie returns, she is oblivious to the fact that Joccy has tampered with the list. She uses a binary search algorithm to find Joccy's test, where she looks at the test in the middle of the pile. If the test is not Joccy's, she binary searches the top half of the list if the test appears after Joccy's name when arranged alphabetically, or the bottom half of the list otherwise. The probability that Maggie finds Joccy's test can be expressed as $\frac{p}{q}$. Compute $p+q$.
train