
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 walk from his home to the gym, which is 4 kilometers away. Initially, he walks $\tfrac{2}{3}$ of the way towards the gym, then he walks $\tfrac{2}{3}$ of the remaining distance back towards his home, and continues this pattern. Find the absolute difference between the two points at which he will oscillate between after walking indefinitely.

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