
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
Given a square with side length s, a rectangle is constructed on one diagonal of the square such that its area equals the area of the square. If the length of the rectangle is the same as the diagonal of the square, find the width of the rectangle.

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