
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
Let \( n \geq 2 \) be an integer. An \( n \times n \) board is initially empty. Each minute, you may perform one of three moves:
1. If there is an L-shaped tromino region of three cells without stones on the board (rotations not allowed), you may place a stone in each of those cells.
2. If all cells in a column have a stone, you may remove all stones from that column.
3. If all cells in a row have a stone, you may remove all stones from that row.

For which \( n \) is it possible that, after some non-zero number of moves, the board has no stones?

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