
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
For any integer \( n \geq 3 \), there exist \( n \) distinct lattice points in the plane, not all on a single line, such that the distance between any two of these points is an integer. There exist infinitely many lattice points in the plane such that any three points are not collinear, and the distance between any two points is not an integer.

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