
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
In a rectangle measuring 3 by 4, 4 points are selected. Find the smallest number $C$ such that, for any selection of these 4 points, the distance between some two of these points does not exceed $C$.

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