
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
Parallelogram $EFGH$ has side lengths of $3$ (for $EF$ and $GH$) and $4$ (for $EG$ and $FH$), with $\angle E = 150^\circ$. Region $S$ consists of all points inside the parallelogram that are closer to vertex $F$ than to any of the other three vertices. What is the area of $S$?
A) 1.5
B) 1.8
C) 2.1
D) 2.4
E) 2.7

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