
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
Consider three side squares of an \(n \times n \times n\) cube that meet at one of the corners of the cube. For which \(n\) is it possible to cover them completely and without overlapping with paper strips of size \(3 \times 1\)? The paper strips can also be glued over the edges of the cube.

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