Simplify the following Boolean expressions, using four$-$variable k$-$maps:

$($a$)A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}D+AB{A}^{\text{'}}+A^{\text{'}}B{C}^{\text{'}}+$ABCD$+A{B}^{\text{'}}C$

$($b$)A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}+BC{B}^{\text{'}}D+A^{\text{'}}{C}^{\text{'}}D+A^{\text{'}}BCD+$ACD.