
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 $z^3 - 27 = 0$ and let $B$ be the set of solutions to $z^2 - 6z + 9 = 0$. Calculate the greatest distance between a point of $A$ and a point of $B$.

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