
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
Inside a right triangle with sides 3 cm, 4 cm, and 5 cm, there are two circles. The ratio of their radii is 9 to 4. The circles are externally tangent to each other and both are tangent to the hypotenuse, with one also tangent to one leg and the other tangent to the other leg. Find the radii of the circles.

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