
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
Seventeen people dine every Saturday night around a round table. How many times is it possible for them to dine if each person wants to have two new neighbors each time? What is the result for eighteen people?

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