
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 $S$ be a finite set of points on the plane, with no three points collinear. Each point in $S$ is colored either blue or red. It is assumed that any triangle whose three vertices are blue contains at least one red point inside, and any triangle whose three vertices are red contains at least one blue point inside. 

Determine the largest possible value of $|S|$.

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