In an uncountable Polish space there is no countably generated $\sigma$-algebra between analytic sets and sets with the Baire property

Question

Let $X$ be an uncountable Polish space. Assume that $\mathcal{A}$ is a $\sigma$-algebra of subsets of $X$ such that every analytic subset of $X$ belongs to $\mathcal{A}$ and every member of $\mathcal{A}$ has the Baire property. Then $\mathcal{A}$ is not countably generated.

I'm not even sure the statement is true, there are occasional mistakes in the book this statement is from.

I'll appreciate any help.