
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
On graph paper (with each square having a side of 1 cm), a rectangle is drawn such that its sides lie along the grid lines, and one side is 5 cm shorter than the other. It turns out that the rectangle can be cut along the grid lines into several pieces and reassembled into a square. What could be the side length of this square? Find all possible values.

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