
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
Consider Sally who starts at her apartment heading towards a park. She walks $\tfrac{2}{3}$ of the distance from her apartment to the park before changing her mind. Initially, the distance to the park is $3$ kilometers. Each time she reaches a point, she decides to walk $\tfrac{2}{3}$ of the distance back toward the previous point (towards apartment when heading to the park or towards the park when heading back). She repeatedly changes her mind at each point. Identify the accumulated difference, $|C-D|$, in kilometers between the two points, $C$ and $D$, where Sally oscillates as she tires of walking.
**A)** $\frac{1}{4}$
**B)** $\frac{1}{2}$
**C)** $\frac{3}{4}$
**D)** $\frac{3}{2}$

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