
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
For which \( n \geq 1 \) can a square grid of size \( n \times n \) be tiled with pieces of the shape:

![](https://cdn.mathpix.com/cropped/2024_05_10_00138f973c2e12c014a0g-146.jpg?height=120&width=163&top_left_y=994&top_left_x=952)

without overlapping or spilling over the edges? (Rotations are allowed.)

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