
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
An arrangement is defined as any way to seat $n$ couples at a round table with $2n$ places. A couple is said to be together if the two members are seated next to each other. What is the average number of couples that are together per arrangement?

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