
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 includes three different male roles, five women audition, and seven men audition. Additionally, there are two roles open to either gender. Determine how many ways there are to cast these five roles if roles can only be filled as per gender specifications.

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