
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
In a plane, there are 12 points such that any three of them are not collinear. Taking any point as the starting point and another point as the endpoint, we create vectors and generate all such vectors. If the sum of the vectors of the three sides of a triangle is the zero vector, we call the triangle a "zero triangle." Find the maximum number of zero triangles that can be formed using these 12 points as vertices.

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