
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 lines parallel to the x-axis or y-axis. Let \( A = (-4, 3) \) and \( B = (4, -3) \). Consider all possible paths of the bug from \( A \) to \( B \) of length at most 24. How many points with integer coordinates lie on at least one of these paths?
A) 253
B) 263
C) 273
D) 283
E) 293

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