
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 500 points inside a convex 1000-sided polygon, along with the polygon's vertices (a total of 1500 points), none of which are collinear, the polygon is divided into triangles with these 1500 points as the vertices of the triangles. There are no other vertices apart from these. How many triangles is the convex 1000-sided polygon divided into?

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