
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
Squares of an  $n \times n$  table ( $n \ge 3$ ) are painted black and white as in a chessboard. A move allows one to choose any  $2 \times 2$  square and change all of its squares to the opposite color. Find all such n that there is a finite number of the moves described after which all squares are the same color.

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