
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 $A$ be the set of solutions to $z^4 - 16 = 0$ and let $B$ be the set of solutions to $z^3 - 8z^2 - 16z + 64 = 0$. What is the greatest distance between a point of $A$ and a point of $B$?
A) $10$
B) $10\sqrt{1.64}$
C) $10\sqrt{2}$
D) $10\sqrt{1 + 0.64\sqrt{2}}$
E) $20$

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