
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
Find all finite sets of points on the plane that have the following property: no three points of the set are collinear, and for any three points of this set, the orthocenter of the triangle formed by these points also belongs to the set.

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