(6) For all real numbers $x, y$ satisfying $|x|+|y| \leqslant 1$, the inequality $\left|2 x-3 y+\frac{3}{2}\right|+|y-1|+|2 y-x-3| \leqslant a$ always holds, then the minimum value of the real number $a$ is $\qquad$.
(6) $\frac{23}{2}$