
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
In two-dimensional space, the one-dimensional measure (circumference) of a circle is $l=2\pi r$, and its two-dimensional measure (area) is $S=\pi r^{2}$. In three-dimensional space, the two-dimensional measure (surface area) of a sphere is $S=4\pi r^{2}$, and its three-dimensional measure (volume) is $V= \dfrac{4}{3}\pi r^{3}$. Using rational reasoning, if in four-dimensional space the three-dimensional measure of a "hypersphere" is $V=8\pi r^{3}$, what is its four-dimensional measure $W$?
A) $2\pi r^{4}$
B) $3\pi r^{4}$
C) $4\pi r^{4}$
D) $6\pi r^{4}$

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