
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
At a social gathering, five couples (ten people) including Charlie and his wife want to sit around two concentric circles - with men on the inner circle and their respective wives directly opposite them on the outer circle. Each couple wants to sit in a way where every man has another man seated directly to his right on the inner circle. How many seating arrangements are available if we count rotations of the inner circle and outer circle independently but do not consider inner to outer circle flips as different?

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