
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
Five points are placed on a sphere of radius 1. What is the largest possible value for the shortest distance between two of the points? Find all configurations for which the maximum is attained.

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