
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, and no two lines are parallel, and no three lines intersect at the same point. These $n$ lines divide the plane into $f(n)$ regions. Then, $f(n+1) = f(n) + \_$.

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