
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
Given that there are 6 points, including the 3 vertices of a triangle and 3 additional points inside the triangle, all of which are not on the same line, find the relationship between the number of non-overlapping triangles formed by these 6 points when three, four, or none of the additional 3 points are collinear with the original triangle.

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