
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
Each of the integers \(1, 2, 3, \ldots, 9\) is assigned to a vertex of a regular 9-sided polygon (every vertex receives exactly one integer from \(\{1, 2, \ldots, 9\}\), and no two vertices receive the same integer) so that the sum of the integers assigned to any three consecutive vertices does not exceed some positive integer \(n\). What is the least possible value of \(n\) for which this assignment can be done?

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