
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 science includes departments of physics, chemistry, and biology. There are three male and three female professors in physics, two male and two female professors in chemistry, and two male and three female professors in biology. A committee of six professors must contain three men and three women and must also include at least one professor from each of the three departments. 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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