
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 square piece of paper with $n$ distinct points inside it, let $M$ represent the set of $n+4$ points consisting of the four vertices of the square and the $n$ points. The square is to be cut into triangles according to the following rules:
(1) Each triangle must have its 3 vertices as elements of the set $M$.
(2) Except for the vertices of the triangle, no other points from the set $M$ should lie within the triangle.
Question: How many triangles can be cut out in total? How many cuts (with each cut being an edge of a triangle) are needed?

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