
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 129-sided polygon is given. Petya and Vasya are playing a game. They take turns marking the vertices of this polygon, with Petya going first. Each time Petya makes a move, he can mark any unmarked vertex. On his turn, Vasya can mark any unmarked vertex that is one away from the last vertex marked by Petya. The game ends when Vasya cannot make a move. What is the maximum number of moves Vasya can guarantee to make regardless of how Petya plays?

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