Let be the set of all complex numbers. Let
$$
\begin{aligned}
& S_1=\{z \in \mathbb{C}:|z-2| \leq 1\} \text { and } \\
& S_2=\{z \in \mathbb{C}: z(1+i)+\bar{z}(1-i) \geq 4\}
\end{aligned}
$$
Then, the maximum value of $\left|\mathbf{z -} \frac{\mathbf{5}}{\mathbf{2}}\right|^2$ for $\mathbf{z} \in \mathrm{S}_1 \cap \mathrm{~S}_2$ is equal to:
