
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 tangent circles are given. A tangent line \( AB \) is drawn to these circles. Another tangent line, parallel to \( AB \), is drawn to the smaller circle, intersecting the larger circle at points \( D \) and \( C \). Given that the radii of these circles are \( R_1 \) and \( R_2 \), find the radius of the circle circumscribing triangle \( BDC \).

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