
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
Let $\omega=-\tfrac{1}{2}+\tfrac{1}{2}i\sqrt3.$ Define $T$ as the set of all points in the complex plane of the form $2a+b\omega+c\omega^2,$ where $0\leq a \leq 2, 0\leq b\leq 2,$ and $0\leq c\leq 2.$ Determine the area of $T$.
A) $2\sqrt{3}$
B) $4\sqrt{3}$
C) $6\sqrt{3}$
D) $8\sqrt{3}$
E) $12\sqrt{3}$

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