
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 contains 1004 points, with 4 located at the vertices, such that any 3 of these points are not collinear. Line segments are drawn between certain points so that the square is subdivided into triangles.

Determine the number of triangles and the number of edges.

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