
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 starts walking from the gym toward his home which is 3 kilometers away. He decides to walk \(\tfrac{2}{3}\) of the distance towards his home. At that point, he changes his mind and walks \(\tfrac{2}{3}\) of the distance remaining back towards the gym. When he reaches that point, he changes his mind again and walks \(\tfrac{2}{3}\) of the distance from there back toward his home. If Henry continues this pattern of walking \(\tfrac{2}{3}\) of the distance from his previous turning point, he will oscillate back and forth between two points \(A\) and \(B\) kilometers away from the gym. What is \(|A-B|\)?
**A)** \(\tfrac{3}{5}\)  
**B)** \(\tfrac{4}{5}\)  
**C)** \(\tfrac{6}{5}\)  
**D)** \(\tfrac{7}{5}\)  
**E)** \(\tfrac{8}{5}\)

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