
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 circle, two chords \( AB = a \) and \( AC = b \) are drawn. The length of the arc \( AC \) is twice the length of the arc \( AB \). Find the radius of the circle.

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