
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
Workers were laying a square floor of size \( n \times n \) using tiles of size \( 2 \times 2 \) and \( 3 \times 1 \). They managed to completely cover the floor using an equal number of tiles of each type. For which \( n \) is this possible? Justify your answer.

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