
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 several lines. In the following situations, the plane can be divided into the maximum number of parts:
(1) When there is one line, it can be divided into a maximum of     parts;
(2) When there are two lines, it can be divided into a maximum of     parts;
(3) When there are three lines, it can be divided into a maximum of     parts;
(4) When there are four lines, it can be divided into a maximum of     parts;
(5) When there are $n$ lines, it can be divided into a maximum of     parts.

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