
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 $z^{4}-16=0$, and let $D$ be the set of solutions to $z^{3} - 27 = 0$. What is the greatest distance between a point of $C$ and a point of $D$?
**A) $\sqrt{8}**$  
**B) $\sqrt{12}**$  
**C) $\sqrt{13}**$  
**D) $6**$

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