Consider a ctm $\mathfrak{M}$ of $ZF+AD^+$. Is it possible to force over $\mathfrak{M}$ to get a model of ZFC which satisfies further the following:

Every projectively definable family of sets of reals has an $OD_a$ member;

Every $OD_a$ set of reals has the property of Baire; Where $a$ is any real parameter.

Here statement 1 is as in my previous question (Projectively definable family of sets of reals).

PS: I am asking this question because there is a paper by Steel & Van Wesep "Two consequences of determinacy consistent with choice" which uses a similar technique.

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