
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 \( n \geq 2 \) be an integer. Given \( n \) points in the plane such that no three are collinear, there exist \( m \) lines such that no line passes through any given point. For any two distinct points \( X \) and \( Y \) among these \( n \) points, there exists a line such that \( X \) and \( Y \) are on opposite sides of the line. Find the smallest positive integer \( m \).

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