
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
In a plane, there are \( n \) lines where any two of the lines intersect, but no three lines pass through the same intersection point. What is the maximum number of new lines obtained by connecting every pair of intersection points that are not already connected by one of the original lines?

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