
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 play has one distinct male role, two distinct female roles, and three distinct roles that can be either gender. One specific man out of six auditioning men has a unique skill required for one of the either-gender roles. Additionally, seven women audition for the parts. In how many ways can the six roles be assigned?

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