The figure below shows a circuit with two NOR gates and two NAND gates. Simplify the function $Y=f(a,b,c,d)$ as much as possible and write the function on SoP$-$form.

$\frac{?}{\text{b}\text{a}\text{r}}(\frac{?}{\text{b}\text{a}\text{r}}(a*b)+(\frac{?}{\text{b}\text{a}\text{r}}(c+(\frac{?}{\text{b}\text{a}\text{r}}(d)))))$

$a*b$

Option $1$

Option $2$

$abc+a\frac{b}{b}ar(d)$