Let \( C \) be the set of all complex numbers. Let
\( S_1=\{z\in \mathbb{C}: |z-2|\leq 1\} \) and
\( S_2=\{z\in \mathbb{C}: z(1+i)+\bar{z}(1-i)\geq 4\} \)
Then, the maximum value of \( \left|z-\dfrac{5}{2}\right|^2 \) for \( z\in S_1\cap S_2 \) is equal to :
