
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
Vasya has picked 8 cells on a chessboard such that no two of them are in the same row or column. On his turn, Petya places 8 rooks on the board, ensuring none of the rooks can attack each other. Then, Vasya points out which rooks are on the preselected cells. If the number of rooks Vasya points out is even (i.e., 0, 2, 4, 6, or 8), Petya wins. Otherwise, all pieces are removed from the board, and Petya makes another move. What is the minimum number of moves needed for Petya to guarantee a win?

(I. Bogdanov)

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