
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
Professors Alpha, Beta, Gamma, and Delta need to choose their chairs from eleven chairs so that each professor is between two students. Calculate the number of ways they can make their chair selection.

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