
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
Solve the equations $z^2 = 3 + 3\sqrt{7}i$ and $w^2 = 5 + 5\sqrt{3}i$ in the complex plane. Determine the area of the parallelogram formed by the vertices which are solutions to both equations.
A) $2\sqrt{6} + 4\sqrt{14}$
B) $2\sqrt{6} + 6\sqrt{14}$
C) $3\sqrt{6} + 8\sqrt{14}$
D) $4\sqrt{6} + 5\sqrt{14}$

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