
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
In a segment with a central angle $\alpha$, an equilateral triangle is inscribed such that one vertex coincides with the midpoint of the chord of the segment, and the other two vertices lie on the arc of the segment. The height of the triangle is $h$. Find the radius of the arc of the segment.

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