
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
In a regular 15-gon, three distinct segments are chosen at random among the segments whose end-points are the vertices. What is the probability that the lengths of these three segments are the three side lengths of a triangle with positive area?
A) $\frac{345}{455}$
B) $\frac{100}{455}$
C) $\frac{310}{455}$
D) $\frac{305}{455}$
E) $\frac{450}{455}$

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