
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
We drew two squares on a graph paper, with side lengths \(m^{2}-n^{2}\) and \(2mn\) cm, where \(m\) and \(n\) are natural numbers. Each side lies along a grid line of the paper, and the distance between grid lines is 1 cm. We want to cut the two squares into pieces so that we can cover a single square with them, and the cutting can only be along the segments of the grid lines. Provide a division that produces as few pieces as possible.

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