
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
a) The radii of two circles \(S_{1}\) and \(S_{2}\) are \(r_{1}\) and \(r_{2}\), and the distance between their centers \(O_{1}\) and \(O_{2}\) is \(d\). What is the minimum distance between points on the circles? What is the maximum distance between points on the circles?

b) Answer the same question with circles \(S_{1}\) and \(S_{2}\) replaced by the discs \(K_{1}\) and \(K_{2}\) bounded by these circles.

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