
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
Twelve chairs are evenly spaced around a round table, numbered clockwise from $1$ through $12$. Six married couples are to sit in the chairs with men and women alternating. No one is to sit either next to, two seats away from, or across from his/her spouse. Additionally, no two men or two women can sit next to each other. How many seating arrangements are possible?
A) 8640
B) 10800
C) 14400
D) 17280
E) 21600

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