
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 particular university, each department within the division of mathematical sciences - which includes mathematics, statistics, and computer science - has three male and three female professors. A committee of six professors is to be formed such that:
- The committee consists of three men and three women.
- The committee includes exactly two professors from each department.
- Each department must be represented by at least one professor of each gender on the committee.
Calculate the number of possible committees that can be formed subject to these constraints.

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