
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, the division of mathematical sciences consists of the departments of mathematics, statistics, and computer science. Each department has three male and three female professors. A committee of eight professors is to be formed containing four men and four women, with each department represented by at least one professor. Find the number of possible committees that can be formed under these conditions.

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