
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 certain university, the division of sciences consists of the departments of mathematics, statistics, computer science, and physics. Each of the first three departments has three male and three female professors, while the physics department has one male and one female professor. A committee of eight professors is to contain four men and four women and must include professors from all four departments such that there are two professors from each of the first three departments and one from the physics department. Find the number of possible committees that can be formed subject to these requirements.

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