
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 two points \( A \) and \( B \) on a plane, there are \( m \) and \( n \) lines through points \( A \) and \( B \) respectively. What is the maximum number of regions that these \( m + n \) lines can divide the plane into? (\( m \neq 0 \) and \( n \neq 0 \)).

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