$($a$)$ Design a Turing Machine that recognizes the following language.

$L_1=\{\begin{array}{ccc}w& in\{a,& b{\}}^{*}\text{:}\end{array}$ Every $a$ is immediately followed by $b)(5$ marks$)$

$($b$)$ Design a Turing Machine that recognizes the following regular express

$(a+b)**aba(ab+a)**(5$ marks $)$