
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
Consider a regular 15-gon where each side's endpoints are amongst the vertices of the polygon. If three distinct segments are chosen randomly among these, calculate the probability that they can form the three sides of a triangle with positive area.

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