
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
Six unit disks \(C_{1}, C_{2}, C_{3}, C_{4}, C_{5}, C_{6}\) are in the plane such that they don't intersect each other and \(C_{i}\) is tangent to \(C_{i+1}\) for \(1 \leq i \leq 6\) (where \(C_{7}=C_{1}\)). Let \(C\) be the smallest circle that contains all six disks. Let \(r\) be the smallest possible radius of \(C\), and \(R\) the largest possible radius. Find \(R-r\).

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