
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
Henry decides to do a workout, starting from his home towards the gym, 3 kilometers away. Initially, he walks $\frac{1}{2}$ of the distance from his home to the gym. At that point, he changes his mind and walks $\frac{1}{2}$ of the distance back toward home. After reaching that spot, he reverses his decision and walks $\frac{1}{2}$ of the distance from there toward the gym. Henry continues this process indefinitely, each time walking $\frac{1}{2}$ of the distance from his current location to either the gym or his home. Determine the absolute difference, $|A-B|$, in kilometers between the two points A and B between which Henry oscillates.
**A) $\frac{1}{2}$**
**B) 1**
**C) 1.5**
**D) 2**

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