
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
A theater company is casting for a play that includes three distinct female roles, one distinct male role, and three roles that are open to any gender. If six men and seven women audition, and one of the female roles is specifically for a lead actress in which only the top three experienced women can qualify, in how many ways can the roles be filled?

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