
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
Míša cut out two identical squares, one rectangle measuring $10 \mathrm{~cm} \times 24 \mathrm{~cm}$, and one more rectangle from paper. What dimensions could this additional rectangle have if it was possible to assemble a square from all four shapes without any overlap? There are several possible rectangles; list at least four.

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