
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
A round table has room for n diners (  $n\ge  2$ ). There are napkins in three different colours. In how many ways can the napkins be placed, one for each seat, so that no two neighbours get napkins of the same colour?

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