
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
In a row of twelve chairs, occupied by five students and four professors (Alpha, Beta, Gamma, Delta), with professors and students alternating, find the number of ways the professors can choose their chairs such that each professor is surrounded on both sides by students or by a student and the ends.

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