
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
Let \( C_{1}, C_{2} \), and \( C_{3} \) be three parallel chords on the same side of the center of a circle. The distance between \( C_{1} \) and \( C_{2} \) is equal to the distance between \( C_{2} \) and \( C_{3} \). The lengths of the three chords are 20, 16, and 8. Given that the three chords are on the same side of the center of the circle and the distances between them are equal, calculate the radius of the circle.

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