
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
Let a convex n-gon \( A_1 A_2 \cdots A_n \) be inscribed in a unit circle. Find the maximum value of the sum of the squares of all its sides and diagonals, and determine when this maximum value is achieved.

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