
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 $n$ be an integer. Define $C_{n}$ as the $n \times $n grid with one diagonal removed. For which integers $n \geq 2$ can $C_{n}$ be tiled using L-shaped tiles consisting of three adjacent cells in the shape of an L (you can rotate the tiles in any direction, but they cannot overlap or extend outside $C_{n}$ or onto the diagonal)?

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