
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
On the sphere \(\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2}=1\right\}\), given \(n (n \geq 2)\) points \(A_{1}, A_{2}, \ldots, A_{n}\), find the maximum possible value of \(\sum_{1 \leq i < j \leq n} \left| A_i A_j \right|^2\).

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