AMC 12 2019b Problem 23

How many sequences of $0$s and $1$s of length $19$ are there that begin with a $0$, end with a $0$, contain no two consecutive $0$s, and contain no three consecutive $1$s?

$\textbf{(A) }55 \textbf{(B) }60 \textbf{(C) }65 \textbf{(D) }70 \textbf{(E) }75$