
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
A square sheet contains 1000 points, with any three points, including the vertices of the square, not being collinear. Connect some of these points and the vertices of the square with line segments to divide the entire square into smaller triangles (using the connected line segments and square edges as sides, and ensuring that no two segments, except at endpoints, share common points). How many line segments are connected in total? How many triangles are formed in total?

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