
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
Three circles are inscribed in an angle - a small one, a medium one, and a large one. The large circle passes through the center of the medium circle, and the medium circle passes through the center of the small circle.

Calculate the radii of the medium and large circles, given that the radius of the small circle is $r$ and the distance from its center to the vertex of the angle is $a$.

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