
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 square $ABCD$ with side length $4$. A smaller secondary square $BEFG$ is placed such that $B$ is a common vertex, and $\angle EBF = 120^\circ$. Region $R$ consists of all points inside the larger square $ABCD$ that are closer to vertex $B$ than any of the other three vertices of the larger square. What is the area of $R$?
A) $8$
B) $4\sqrt{3}$
C) $12$
D) $16$
E) $10$

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