
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
Given is a natural number  $n>4$ . There are  $n$  points marked on the plane, no three of which lie on the same line. Vasily draws one by one all the segments connecting pairs of marked points. At each step, drawing the next segment  $S$ , Vasily marks it with the smallest natural number, which hasn't appeared on a drawn segment that has a common end with  $S$ .  Find the maximal value of  $k$ , for which Vasily can act in such a way that he can mark some segment with the number  $k$ ?

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