
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 natural number \( n > 4 \) is given. There are \( n \) points marked on a plane, no three of which lie on the same straight line. Vasiliy connects all pairs of marked points with line segments, one at a time. Each time he draws a new segment \( S \), he labels it with the smallest natural number that has not yet been assigned to any segment sharing a common endpoint with \( S \). For what largest \( k \) can Vasiliy ensure that some segment is labeled with the number \( k \)?

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