
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 an isosceles triangle with a $120^{\circ}$ angle, the radius of the inscribed circle is $R$. Inside the triangle, there are two equal circles that touch each other, where each circle touches one of the legs of the triangle and the inscribed circle. Find the radii of these circles (find all solutions).

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