
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 $z^{4}-4z^{3}-16z^2+64z=0$. Find the greatest distance between a point of A and a point of B.

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