
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
In how many ways can four couples sit around a round table such that no two women sit next to each other? How many arrangements are possible if we want no two spouses, no two women, and no two men to sit next to each other?

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