
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
A right circular cone, a right circular cylinder, and a sphere all have the same radius $r$. The height of the cone and the cylinder is equal to the radius of the sphere. Given the volumes of these shapes as $A$, $M$, and $C$ respectively, determine the relationship between these volumes.
A) $2 \pi r^3$
B) $\frac{1}{3} \pi r^3$
C) $\pi r^3$
D) $\frac{4}{3} \pi r^3$
E) $\frac{4}{9} \pi r^3$

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