
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
Given that there are three professors (Alpha, Beta, and Gamma) and seven students, and the professors arrive before the students, determine the number of ways the professors can choose their chairs such that each professor will have at least two students between them.

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