
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 a triangular paper with 1 point inside, and including the triangle's vertices, there are a total of 4 points. If any three of these points are not collinear, triangles can be formed using these 4 points as vertices. Cutting the paper into these triangles results in 3 smaller triangles. If there are 2 points inside the triangular paper, making a total of 5 points with the vertices, and again any three of these points are not collinear, cutting the paper into triangles results in 5 smaller triangles, and so on. By following this pattern, if there are 15 points inside the triangular paper, combined with the triangle’s vertices to total 18 points, and no three points are collinear, how many smaller triangles are formed when the paper is cut into triangles? Answer with a number.

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