
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 seven students and Professors Alpha, Beta, Gamma, and Delta. These four professors arrive before the seven students and decide to choose their chairs so that each professor will be between two students. How many ways can Professors Alpha, Beta, Gamma, and Delta choose their chairs?

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