
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
Any seven points are taken inside or on a rectangle with side lengths $1$ and $2$. Determine the smallest possible number $b$ such that it is always possible to select one pair of points from these seven 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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