
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 of a circle is at a distance \( h \) from the center. In each of the segments subtended by the chord, a square is inscribed such that two adjacent vertices of the square lie on the arc, and the other two lie on the chord or its extension. What is the difference in the side lengths of these squares?

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