
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
Given two circles that do not intersect, construct a right-angled triangle whose hypotenuse is the common external tangent of the two circles. The legs of the triangle should each be tangent to one of the given circles, and one of the common internal tangents of the two circles should pass through the right-angle vertex of the triangle.

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