
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
In a right-angled triangle, the hypotenuse is \( c \). The centers of three circles with radius \( \frac{c}{5} \) are located at the vertices of the triangle. Find the radius of the fourth circle, which touches the three given circles and does not contain them within itself.

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