
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 \( z^{4} = 16 \) and let \( B \) be the set of solutions to \( z^{4} - 16z^{3} + 64z^{2} - 128z + 256 = 0 \). What is the greatest distance between a point of \( A \) and a point of \( B \)?
A) \( 4 \)
B) \( 2\sqrt{5} \)
C) \( 6 \)
D) \( 4\sqrt{2} \)
E) \( 8 \)

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