
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 go to the gym which is $3$ kilometers away from his home. Initially, he walks $\frac{2}{3}$ of the way towards the gym. Then he changes his mind and walks $\frac{2}{3}$ of the distance from that point back towards his home. He continues this pattern, walking $\frac{2}{3}$ of the distance toward his last destination each time he changes his mind. If he continues indefinitely, let $C$ and $D$ be the distances from his home to the two points between which he will oscillate. Calculate $|C-D|$.

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