
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 the greatest possible integer  $n$  such that one can place  $n$  points in a plane with no three on a line, and color each of them either red, green, or yellow so that:
(i) inside each triangle with all vertices red there is a green point.
(ii) inside each triangle with all vertices green there is a yellow point.
(iii) inside each triangle with all vertices yellow there is a red point.

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