
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  $E$  be a set of  $n$  points in the plane  $(n \geq 3)$  whose coordinates are integers such that any three points from  $E$  are vertices of a nondegenerate triangle whose centroid doesnt have both coordinates integers. Determine the maximal  $n.$ 

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