
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, among which no two are parallel and no three are concurrent. How many intersections are there among these lines? How many triangles can be formed? Into how many regions is the plane divided by these lines? How many of these regions are unbounded?

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