
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 non-overlapping circles are positioned such that one of their common internal tangents is perpendicular to one of their common external tangents. Find the area of the triangle formed by these tangents and the third common tangent of the given circles if their radii are \( r_1 \) and \( r_2 \).

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