In a coordinate plane, point $A$ is located at $(3, 4)$ and point $B$ is located at $(7, 8)$. The line segment $\overline{AB}$ is reflected over the $y$-axis to create segment $\overline{A'B'}$. What is the sum of the coordinates of the midpoint of segment $\overline{A'B'}$? Let's think step by step and output the final answer within \boxed{}.
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