Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>Given figure $A B C D$, with $\overline{A B} \| \overline{D C}, m \angle B=60, m \angle D=45, B C=8$
and $A B=24,$ find the perimeter.