
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
One thousand points form the vertices of a convex 1000-sided polygon, with an additional 500 points inside such that no three of the 500 are collinear. This 1000-sided polygon is triangulated in such a way that all the given 1500 points are vertices of the triangles and these triangles have no other vertices. How many triangles are formed by this triangulation?

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