
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 \( n \) points in a plane, where no three points are collinear, some pairs of points are connected by line segments. If there is no triangle formed by the connected line segments, then the total number of connected line segments does not exceed \(\left\lfloor \frac{n^{2}}{4} \right\rfloor\).

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