
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 $\omega = -\frac{1}{2} + \frac{1}{2}i\sqrt3,$ and consider the set $T$ in the complex plane represented by the points of the form $p+q\omega+r\omega^2,$ where $0 \leq p \leq 2, 0 \leq q \leq 1,$ and $0 \leq r \leq 1.$ What is the area of $T$?
A) $\frac{\sqrt{3}}{2}$
B) $\sqrt{3}$
C) $\frac{3\sqrt{3}}{2}$
D) $\frac{3}{2}$

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