
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
Consider a $5-12-13$ right triangle where the vertices are the centers of three mutually externally tangent circles. The radius of the circle at the right-angle vertex is half the radius of the circle at the vertex opposite the shortest side. What is the sum of the areas of these circles?

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