
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 starts at point $A = (-2, 3)$ in the coordinate plane and moves to point $C = (4, -3)$, the bug can only traverse paths parallel to the $x$-axis or $y$-axis, and it must use paths of length at most 25 units, 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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