
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 $n$ lines on a plane, any two of which are not parallel, and no three of which intersect at the same point, how many intersection points do these $n$ lines have?

Continuing from the previous problem, if we require these $n$ lines to partition the plane, how many non-overlapping regions will be formed?

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