
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
Inside a convex $n$-gon there are 100 points positioned in such a way that no three of these $n+100$ points are collinear. The polygon is divided into triangles, each having vertices among any 3 of the $n+100$ points. For what maximum value of $n$ can no more than 300 triangles be formed?

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