
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
Given the isosceles right triangle $ABC$ with $CA=CB=b$. Inside the triangle, there are three mutually externally tangent circles $k_{1}, k_{2}, k_{3}$. Circle $k_{1}$ is tangent to the two sides originating from vertex $A$, similarly, $k_{2}$ is tangent to the sides originating from vertex $B$, and $k_{3}$ is tangent to the sides originating from vertex $C$. Calculate the radii of the circles. Verify the calculation with a drawing, taking $b$ to be $20 \mathrm{~cm}$.

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