
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 the complex plane, let $C$ be the set of solutions to $z^{3} - 27 = 0$ and let $D$ be the set of solutions to $z^{3} - 9z^{2} + 27z - 27 = 0$. What is the greatest distance between a point of $C$ and a point of $D$?
**A)** $\frac{9}{2}$  
**B)** $9$  
**C)** $\frac{9\sqrt{2}}{2}$  
**D)** $9\sqrt{2}$  
**E)** $18$

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