
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Four mathematicians, two physicists, one chemist, and one biologist take part in a table tennis tournament. The eight players are to compete in four pairs by drawing lots. What is the probability that no two mathematicians play against each other?

Present the answer in LaTex format: \boxed{Your answer}
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