Available at major population centres of the Negentropic polity are private chambers called the "Mantle of the Judge". These are small areas allowing normal citizens to bring their problems before the Judge and ask for Eir Judgement on the actions. This is a strictly voluntary activity, and in no way binds the baseline to performing a given action. This type of facility is often difficult to find, the logic being the more severe the problem the more likely the baseline is to expend the required effort to find the Mantle.
The Mantle is a simple room with a somewhat-comfortable chair and a coat rack, carrying the Mantle itself. The person enters, sits, and places the Mantle about their shoulders. The next thing they know they're putting the Mantle back onto the coat rack. They will have a memory of a conversation with the Judge in a sort of lucid dream- state indicating the issues involved with the problem (explained in terms that particular sophont can comprehend) and the Judge's recommendation as to how best to handle the issue.
Note that this may or may not be in the best interest of the baseline asking the question! Instead, the Judge's recommendations are based first on the Negentropic Principles, followed by society's best interest, and finally the individual.