
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 two different male roles, two different female roles, and three different roles that can be either gender. Only a man can be assigned to a male role, and only a woman can be assigned to a female role. If six men and seven women audition, in how many ways can the seven roles be assigned?

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