Definable $(p,q)$-theorem for NIP formulas

Assume that the formula $\phi(x;y)$ is NIP. Let $M$ be a model and let $\phi(x;b)\in L(\mathcal U)$ be non-dividing over $M$. Definable $(p,q)$-conjecture. There is a formula $\psi(y)\in \operatorname{tp}(b/M)$ such that the partial type

$$\{\phi(x;b):b\in \psi(M)\}$$

is consistent. This was presented as a definable version of the $(p,q)$-theorem and was stated as an open conjecture in the paper.