
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 three departments: mathematics, statistics, and computer science. Each department has three male and three female professors. A committee of six professors is to be formed, including three men and three women. Additionally, the committee must have at least two members from each department, and at least one member must be a senior professor. Find the number of possible committees that can be formed given these requirements.

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