
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
We have an \(n\)-gon, and each of its vertices is labeled with a number from the set \(\{1, \ldots, 10\}\). We know that for any pair of distinct numbers from this set, there is at least one side of the polygon whose endpoints have these two numbers. Find the smallest possible value of \(n\).

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