
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 \( r_{1} \) and \( r_{2} \) touch each other externally. The segment of their common external tangent that lies between the points of tangency is rotated around the line through the centers of the circles. Express the lateral surface area of the resulting truncated cone in terms of \( r_{1} \) and \( r_{2} \).

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