
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
Let \( S \) be a set of 2017 distinct points in the plane. Let \( R \) be the radius of the smallest circle containing all points in \( S \) on either the interior or boundary. Also, let \( D \) be the longest distance between two of the points in \( S \). Let \( a, b \) be real numbers such that \( a \leq \frac{D}{R} \leq b \) for all possible sets \( S \), where \( a \) is as large as possible and \( b \) is as small as possible. Find the pair \( (a, b) \).

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