
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
The four complex roots of the equation
\[ z^4 + 4iz^3 + (-4 + 4i)z^2 + (-8 - i)z + (2 - 8i) = 0, \]
when plotted in the complex plane, form a rectangle. Find the area of the rectangle.

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