
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 the same university, the division of mathematical sciences has expanded to include four departments: mathematics, statistics, computer science, and data science. Each department has three male and three female professors. A new committee of eight professors is to be formed with four men and four women, including exactly two professors from each of the four 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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