
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
The circles with radii \( R \) and \( r \) touch each other externally. The lateral sides of an isosceles triangle are their common tangents, and the base of the triangle touches the larger of the circles. Find the base of the triangle.

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