
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 \( n(n \geqslant 3) \) points \( A_{1}, A_{2}, \cdots, A_{n} \) on a plane such that no three points are collinear. Let \( \alpha \) denote the minimum value of all angles \( \angle A_{i} A_{j} A_{k} \) where \( A_{i}, A_{j}, A_{k} \) are three different given points. For each \( n \), find the maximum value of \( \alpha \) and determine how these points should be distributed to achieve this maximum value.

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