
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 typical triangle is defined as one in which each angle is at least \(30^{\circ}\).

A triangle is identified using the following procedure. The perimeter of a circle is divided into 180 equal arcs, and 3 distinct points are randomly chosen from these division points. (Any three points are chosen with equal probability.) What is the probability that the selected points form a typical triangle?

What is the probability of selecting a typical triangle if the vertices can be chosen arbitrarily on the perimeter of the circle?

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