
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
During his morning run, Jake decides to jog towards the park, located $4$ kilometers away from his home. He jogs $\frac{1}{2}$ of the way and changes his mind, then jogs $\frac{1}{2}$ of the way back home. He continues this pattern, always jogging $\frac{1}{2}$ of the distance towards his next destination. When he keeps alternating between jogging toward the park and home, he fluctuates between a point $C$ kilometers from home and a point $D$ kilometers from home. What is $|C-D|$?
A) $\frac{1}{3}$
B) $\frac{2}{3}$
C) $1$
D) $\frac{4}{3}$

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