
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 his home towards a gym 3 kilometers away. He walks $\frac{2}{3}$ of the current distance from his current position toward his destination each time before changing his mind. At each change of mind, his target switches between the gym and home. Determine the distance between the two points A and B that Henry oscillates between.

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