
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
Let \( p_{1}, p_{2}, \cdots, p_{n} \) be \( n \) points in the plane, with no three points collinear. These points are connected by \( m \) line segments such that any set of 4 points contains 3 points that form a triangle. In other words, among these 3 points, each pair is connected by a segment. Find the minimum value of \( m \).

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