
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 different university, the department of natural sciences consists of the physics, chemistry, and biology departments. Each department has three male and three female professors. A committee is to be formed with four men and four women. Additionally, the committee must include:
- At least one professor from each gender in each department,
- Exactly three professors from any one department.
Find the number of possible committees that can be formed following these conditions.

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