
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 on a plane, where no three points are collinear. These points are connected by \( m \) line segments such that among any four points, there are always three points that form a triangle, meaning each pair of these three points is connected by a line segment. Find the minimum value of \( m \).

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