
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 $\omega = e^{2\pi i / 4} = i$, which is a fourth root of unity. Define the set $T$ in the complex plane consisting of all points of the form $a + b\omega + c\omega^2$ where $0 \leq a \leq 2$, $0 \leq b \le 1$, and $0 \leq c \le 2$. Determine the area of the set $T$.
A) $\frac{4}{3}$
B) $\frac{1}{2}$
C) $2$
D) $3$
E) $\frac{\sqrt{3}}{2}$

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