Beta-Binomial Moments via Adam's and Eve's Laws

Let $P \sim \operatorname{Beta}(2, 3)$ and, given $P = p$, let $X \sim \operatorname{Binomial}(10, p)$. Using Adam's law ($E[X] = E[E[X \mid P]]$) and Eve's law ($\operatorname{Var}(X) = E[\operatorname{Var}(X \mid P)] + \operatorname{Var}(E[X \mid P])$), derive $E[X]$ and $\operatorname{Var}(X)$.