
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
George is planning a larger gala dinner for five other couples, his wife, and himself. He plans to seat the six couples around a circular table for 12, ensuring that each husband sits directly opposite his wife. How many different seating arrangements can he make, if rotations and reflections of each seating arrangement are considered identical?

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