
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
Four circles of radius \( r \) and \( R \) (with \( R > r \)) are arranged such that three smaller circles (all of radius \( r \)) are mutually externally tangent to each other and internally tangent to a larger circle of radius \( R \). The fourth small circle (radius \( r \)) is placed such that it is externally tangent to two of the smaller circles and internally tangent to the larger circle. What is the radius \( R \) of the large circle in terms of \( r \)?

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