The Constitution says that Presidential appointments (e.g. Cabinet members, federal judges, SCOTUS Justices) are made with the advice and consent of the Senate. I've seen many hearings and votes on approving such nominations -- this is "consent". Are there examples of the Senate providing official advice to the President on who to nominate?
I imagine that he can contact anyone he wants to discuss potential nominations, so why would this need to be enumerated in the Constitution? So I'm asking if POTUS receives advice from Senate through a formal process, not senators taking it upon themselves to publish their opinions (traditionally in newspaper op-eds, nowadays more likely on Twitter).
Or did "advice and consent" mean something else to the framers in this context?