
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
The \( n \) points \( P_{1}, P_{2}, \ldots, P_{n} \) are placed inside or on the boundary of a disk of radius 1 in such a way that the minimum distance \( d_{n} \) between any two of these points has its largest possible value \( D_{n} \). Calculate \( D_{n} \) for \( n=2 \) to \( 7 \) and justify your answer.

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