
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
Every single point on the plane with integer coordinates is coloured either red, green or blue. Find the least possible positive integer  $n$  with the following property: no matter how the points are coloured, there is always a triangle with area  $n$  that has its  $3$  vertices with the same colour.


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