I have two questions about universally measurable sets:

(1) Is there a universally measurable set of reals which does not have the Baire property?

(2) Is there a universally measurable set of reals which is not universally Baire?

Note that a Luzin set is universally measurable (null) but it does not have the Baire property so these are consistent. But are there ZFC examples?

Recall that a set of reals $A$ is universally measurable if for every Borel (probability) measure $m$ on reals, $A$ equals some Borel set modulo an $m$-null set. $A$ is universally Baire if for every topological space $X$ and continuous function $f: X \rightarrow \mathbb{R}$ the preimage $f^{-1}[A]$ has the Baire property in $X$ (equals an open set modulo meager). Also, universally Baire set are universally measurable.

Thanks!