
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
(1) There are 12 people to be seated at two tables, with 6 people at each table, sitting around a circular table. How many different seating arrangements are there?

(2) If there are 12 couples to be evenly divided into two tables, sitting around a circular table, how many different seating arrangements are there?

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