
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, none of which are parallel, and no three of which intersect at the same point. Let $k$ ($k<n$) be the number of such lines that divide the plane into $f(k)$ regions. Determine the difference between the number of regions formed by $k+1$ lines and the number of regions formed by $k$ lines.

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