
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 community theater is holding auditions for a new play that has three different male roles, three different female roles, and four different roles that can be either gender. If seven men and eight women audition, in how many ways can the ten roles be assigned?

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