
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 \( A_{1}, A_{2}, \cdots, A_{n} \) on a plane (\( n \geq 3 \)), where no three points are collinear. Out of these points, \( K \) point pairs are chosen to determine \( K \) lines (i.e., drawing a line through each pair of points among the \( K \) point pairs). These \( K \) lines do not intersect to form a triangle where all three vertices are among the given points. Find the maximum value of \( K \).

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