
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 points are placed inside or on a circle with a diameter of 1 unit. Determine \( b \), the smallest possible number such that it is always possible to select one pair of points from these six such that the distance between them is equal to or less than \( b \).

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