
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
Two players play the following game on an $n \times n$ chessboard. Each square has a disk placed on it, with one side red and the other side blue. The players take turns. On a player's turn, they select a blue disk and in the rectangle defined by the selected disk as the top-left corner and the bottom-right corner of the board, every disk is flipped. A player loses if they cannot make a move.

Which initial positions allow the starting player to have a winning strategy?

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