
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
Two circles with radii \( r \) and \( R \) touch each other internally. Find the side of an equilateral triangle where one vertex is at the point of tangency of the given circles, and the other two vertices lie on the different given circles.

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