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
After the World Hockey Championship, three journalists wrote articles about the German team - each for their own newspaper.

- The first wrote: "The German team scored more than 10 but less than 17 goals throughout the championship."
- The second wrote: "The German team scored more than 11 but less than 18 goals throughout the championship."
- The third wrote: "The German team scored an odd number of goals throughout the championship."
  
It turned out that only two of the journalists were correct. How many goals could the German team have scored in the championship? List all possible options.
user
[11, 12, 14, 16, 17]
rule
After the World Hockey Championship, three journalists wrote articles about the German team - each for their own newspaper.

- The first wrote: "The German team scored more than 10 but less than 17 goals throughout the championship."
- The second wrote: "The German team scored more than 11 but less than 18 goals throughout the championship."
- The third wrote: "The German team scored an odd number of goals throughout the championship."
  
It turned out that only two of the journalists were correct. How many goals could the German team have scored in the championship? List all possible options.
train