
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
Two circles with radii \(R\) and \(r\) are tangent to the sides of a given angle and to each other. Find the radius of a third circle that is tangent to the sides of the same angle and whose center is at the point of tangency of the two circles.

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