
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  $2017$  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  $a\le \frac{D}{R}\le b$  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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