
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
\(A_{1} A_{2} \cdots A_{n}\) is a regular \(n\)-gon inscribed in the unit circle. \(P\) is any point on the circumference of the unit circle. Then \(\sum_{1 \leq i < j \leq n} \left| A_{i} A_{j} \right|^{2} = \quad.\)

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