
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
Twelve people sit down at random seats around a round table. Five of them are math majors, four others are physics majors, and the three remaining people are biology majors. What is the probability that all five math majors sit in consecutive seats?

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