
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
Consider the complex numbers $A$ and $B$ defined as the set of solutions to the equations $z^{4} - 16 = 0$ and $z^{4} - 8z^{3} +18z^{2} - 27z + 27=0$, respectively. Find the greatest distance between any point in set $A$ and any point in set $B$.
A) $\sqrt{5}$
B) $\sqrt{10}$
C) $\sqrt{13}$
D) $\sqrt{17}$

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