
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
Find all positive integers \( n \) (where \( n \geq 3 \)) such that for an \( n \times n \) grid, after removing any one square, the remaining grid can always be cut into L-shaped pieces. An L-shaped piece is defined as a \( 2 \times 2 \) grid with one small square removed, leaving a piece composed of three small squares.

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