
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 a set \(T\) in the complex plane with points of the form \(2a+b\omega+c\omega^2,\) where \(0 \leq a \leq 1, 0 \leq b \leq 1,\) and \(0 \leq c \leq 1.\) Determine the area of \(T\).
A) \(1\sqrt{3}\)
B) \(2\sqrt{3}\)
C) \(3\sqrt{3}\)
D) \(4\sqrt{3}\)
E) \(6\sqrt{3}\)

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