
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
Ten chairs are evenly spaced around a round table, numbered clockwise from 1 through 10. Find the number of seating arrangements for five married couples that have men and women alternating, and no one is sitting either next to or across from their spouse.

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