
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
In a plane geometry setup, four equilateral triangles each with side length $4$ and three squares each with side length $4$ are placed alternatively on the same straight line. Each square is connected to the next triangle such that one vertex of the square is touching a vertex of the triangle. Calculate the total area covered by the union of these shapes, given the overlap is solely at the vertices.
A) $64\sqrt{3}$
B) $64$
C) $16\sqrt{3} + 48$
D) $48\sqrt{3}$

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