
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
An n-gon (which is not self-intersecting) is triangulated using m interior vertices. In other words, there is a set of N triangles such that: 
1. Their union is the original n-gon; 
2. The union of their vertices is the set consisting of the n vertices of the n-gon and the m interior vertices; 
3. The intersection of any two distinct triangles in the set is either empty, a vertex of both triangles, or a side of both triangles. 

What is N?

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