Three-Layer Poisson-Binomial-Uniform Tower

Let $U \sim \operatorname{Uniform}(0,1)$. Given $U$, let $N \mid U \sim \operatorname{Poisson}(10U)$. Given $(N, U)$, let $X \mid N, U \sim \operatorname{Binomial}(N, U)$.

Using iterated tower properties and Eve's law, find $E[X]$ and $\operatorname{Var}(X)$.