
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
8. In a convex $n$-gon, all diagonals are drawn. Find the maximum possible number of their intersection points.

9. Inside a convex $n$-gon, $m$ points are given. Connect these points with segments to each other and to the vertices of the polygon such that each of the given points is the vertex of a triangle and the resulting triangles do not have common internal points. Into how many triangles will the polygon be divided?

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