
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 right triangle \(ABC\) with angle \(A\) equal to \(30^{\circ}\), a circle with radius \(R\) is inscribed. A second circle, lying outside the triangle, touches the side \(BC\) and the extensions of the other two sides. Find the distance between the centers of these circles.

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