
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 \( \omega = -\frac{1}{2} + \frac{i\sqrt{3}}{2} \). Consider the set \( T \), representing all points in the complex plane of the form \( a + b\omega + c\omega^2 \), where \( 0 \leq a, b, c \leq 2 \). Determine the area of \( T \).
A) \( 3\sqrt{3} \)
B) \( 4\sqrt{3} \)
C) \( 5\sqrt{3} \)
D) \( 6\sqrt{3} \)
E) \( 7\sqrt{3} \)

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