
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
Rhombus \( EFGH \) has side length \( 4 \) and \( \angle F = 150^\circ \). Region \( S \) consists of all points inside the rhombus that are closer to vertex \( F \) than any of the other three vertices. What is the area of \( S \)?
**A) \( \frac{3\sqrt{3}}{3} \)**  
**B) \( \frac{4\sqrt{3}}{3} \)**  
**C) \( \frac{5\sqrt{3}}{3} \)**  
**D) \( 2 + \frac{\sqrt{3}}{3} \)**  
**E) \( 4 \)**

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