
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 departments of mathematics, statistics, and computer science. Each department has three male and three female professors. A committee of six professors is to contain three men and three women and must also include at least one professor from each department but no more than two from any single department. How many possible committees can be formed under these new conditions?

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