
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
A triangle with sides $6$, $8$, and $10$ is a right triangle. The vertices of this triangle are the centers of three circles that are mutually externally tangent to each other. What is the sum of the areas of these circles?

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