
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
A bug travels in the coordinate plane, moving only along paths parallel to the x-axis or y-axis. Let \(A = (-4, 3)\) and \(B = (4, -3)\), and there is a rectangle which the bug cannot enter delimited by corners at \((-1, 1)\), \((1, 1)\), \((1, -1)\), and \((-1, -1)\). Calculate all possible integer coordinate points \( (x, y) \) that the bug can reach on its path from \(A\) to \(B\) assuming the maximum allowable path length is 24.
A) 80
B) 96
C) 110
D) 120
E) 140

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