
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 intersection of great circles. It is known that on a sphere, \( n \) great circles intersect at \( n(n-1) \) points in the general case. How should the numbers \( 1, 2, \ldots, n(n-1) \) be arranged at these points so that the sums of the numbers located on each circle are equal? (Recall that great circles lie in planes passing through the center of the sphere.)

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