
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
We consider 100 points in the plane, such that no three of them are collinear. We draw all the lines passing through any two of these points, and suppose that if \(A, B, C, D\) are four of these points, then \((AB)\) and \((CD)\) are not parallel, and their point of intersection is not located on another line. How many regions of the plane are formed by these lines?

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