
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
One circle is circumscribed around an equilateral triangle \(A B C\), and another circle is tangent to lines \(A B\) and \(A C\) and the first circle. Find the ratio of the radii of the circles.

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