
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 polygon with 1000 sides. Inside it, 500 points are taken and connected with each other and the vertices of the polygon. How many triangles are formed? (The sides of the triangles do not intersect).

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