
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

There are 5 empty glasses in a row on a table. Petya and Vasya take turns (starting with Petya) to pour drinks into the glasses: Petya pours lemonade, and Vasya pours compote. In one turn, a player can fill one empty glass of their choice so that no two adjacent glasses have the same drink after their move. If all glasses are filled as a result of the players' actions, the game ends in a draw. Otherwise, the player who cannot make a move loses. For which `p` will Vasya win regardless of Petya's actions?

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