
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 that a bug travels in the coordinate plane, moving only along the lines that are parallel to the x-axis or y-axis, and paths from A = (-2, 3) to B = (4, -3) of length at most 24, determine the number of points with integer coordinates that lie on at least one of these paths.

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