
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 certain institute, the division of science consists of four departments: physics, chemistry, biology, and mathematics. Each department has three male and three female professors. A committee of eight professors is to be formed with four men and four women, and must also include exactly two professors from each of two departments and two professors (one male and one female) from the other two departments.

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