
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
Eleven chairs in a row are to be occupied by eight students and Professors Alpha, Beta, and Gamma. These three professors arrive before the eight students and decide to choose their chairs so that each professor will be between two students. Determine the number of ways in which Professors Alpha, Beta, and Gamma can choose their chairs.

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