Let $\mathrm{S}=\{z: 3 \leq 2 z-3(1+\mathrm{i}) \mid \leq 7\}$ be a set of complex numbers.
Then $\left.\operatorname{Min}_{z \in S}\left(z+\frac{1}{2}(5+3 i)\right) \right\rvert\,$ is equal to :
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