
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 legs of a right triangle are 6 and 8. Semicircles are constructed on all its sides as diameters, lying outside the triangle. Find the radius of the circle tangent to the constructed semicircles.

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