
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 Henry walks $\frac{2}{3}$ of the remaining distance towards his gym or home from the point where he last changed his mind, and this process continues indefinitely, determine the absolute difference between the distances of points $A$ and $B$ from Henry's home.

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