
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
Given a board consists of  $n \times n$  unit squares ( $n \ge 3$ ). Each unit square is colored black and white, resembling a chessboard. In each step, TOMI can choose any  $2  \times 2$  square and change the color of every unit square chosen with the other color (white becomes black and black becomes white). Find every  $n$  such that after a finite number of moves, every unit square on the board has a same color.

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