
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 a circle of radius \( R \). Four circles of equal radii are tangent to the given circle externally, and each of these four circles is tangent to two others. Find the radii of these four circles.

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