
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
Around the edge of a round table, there are $n$ empty glasses (with $n \geq 3$). Petya and Vasya take turns (starting with Petya) pouring kvass into one of the glasses. On his turn, Petya pours kvass into an empty glass that has both adjacent glasses either both empty or both full. On his turn, Vasya pours kvass into an empty glass that has one adjacent glass empty and the other full. The player who cannot make a move loses. For which values of $n$ will Petya win regardless of Vasya's actions?

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