
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, there are three departments in the science division: physics, chemistry, and biology, each with three male and three female professors. A committee of six professors is to be formed with an equal number of men and women and must also include two professors from each of the three departments. Determine how many different committees can be formed under these conditions.

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