
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 spheres with radius \( r \) are externally tangent to each other. Three spheres with radius \( R \) are externally tangent to each other, with each one tangent to the other two. Each of these spheres is also externally tangent to the first two spheres.

Find the relationship between \( R \) and \( r \).

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