
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 10 points in the plane where no three points are collinear, we draw 4 line segments, each connecting two points on the plane. The choice of these line segments is arbitrary, and each line segment has an equal chance of being chosen. Find the probability that any three of these line segments will form a triangle with vertices among the given 10 points. Express this probability in the form \(\frac{m}{n}\), where \(m\) and \(n\) are coprime positive integers. Determine \(m+n\).

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