
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 selected 8 squares on a chessboard such that no two squares are in the same row or column. On his turn, Petya places 8 rooks on the board in such a way that none of them attack each other, and then Vasya points out all the rooks that are standing on the selected squares. If the number of rooks pointed out by Vasya on this turn is even (i.e., 0, 2, 4, 6, or 8), Petya wins; otherwise, all pieces are removed from the board and Petya takes the next turn. What is the minimum number of turns in which Petya can guarantee a win?

(I. Bogdanov)

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