
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
Consider rhombus $EFGH$ where each side length is $3$ and $\angle E = 150^\circ$. Region $S$ includes all points inside the rhombus that are closer to vertex $E$ than any other vertices $F$, $G$, or $H$. Determine the area of region $S$.
A) $\frac{3}{2}$
B) $2 \sqrt{3}$
C) $\frac{9}{4}$
D) $\frac{9}{2}$
E) $\frac{3\sqrt{3}}{2}$

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