
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
A chord is at a distance $h$ from the center of a circle. In each of the two segments of the circle formed by this chord, a square is inscribed such that a pair of its adjacent vertices lie on the chord, and the other pair of adjacent vertices lie on the corresponding arc of the circle. Find the difference in the side lengths of the squares.

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