
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
1. Inside a triangular piece of paper, there is 1 point, making a total of 4 points including the vertices of the triangle. Given that any three of these points are not collinear, triangles are formed using these 4 points as vertices, and the paper is cut into smaller triangles, resulting in 3 small triangles.
2. Inside a triangular piece of paper, there are 2 points, making a total of 5 points including the vertices of the triangle. Given that any three of these points are not collinear, triangles are formed using these 5 points as vertices, and the paper is cut into smaller triangles, resulting in 5 small triangles.
... Following this pattern, if there are 2012 points inside a triangular piece of paper, making a total of 2015 points including the vertices of the triangle, and given that any three of these points are not collinear, triangles are formed using these points as vertices, and the paper is cut into smaller triangles, then the number of such small triangles is $\boxed{4025}$ (answer in digits).

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