
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
At a university, the division of science consists of three departments: Physics, Chemistry, and Biology. Each department has three male and three female professors. A committee of six professors is to be formed that includes three men and three women and must also have two professors from each of the three departments. Determine the number of possible committees that can be formed under these conditions.

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