
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
Rectangle $ABCD$ has dimensions where $AB = 2$ and $BC = 4$, and $\angle B = 120^{\circ}$. Find the area of the region $R$ consisting of all points inside the rectangle that are closer to vertex $B$ than any of the other three vertices.

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