
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
Given \( n(>2) \) distinct points in space, consider all the lines determined by pairs of these points, and then all the angles formed by pairs of these lines. It is observed that the smallest angle (one of the smallest) among these angles is exactly \( 60^{\circ} \). What could be \( n \)?

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