
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
$B$ and $C$ play the following game. $B$ places a queen on one of the squares in the top row of an $n \times n$ chessboard. Then they take turns moving the queen according to chess rules, but they can only move the piece to a square that is closer to the bottom-left corner than the square it was previously on. $C$ moves first. The player who is forced to move the piece to the bottom-left corner loses. Who wins for $n=8$? Find an $n$ such that the other player has a winning strategy.

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