
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 sciences consists of three departments: physics, chemistry, and biology. Each department has three male and three female professors. A committee of six professors needs to be formed such that it includes exactly four women and two men, with at least one professor from each department. Additionally, at least one member from the committee must be from the biology department. Find the number of possible committees that can be formed under these requirements.

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