I think ideally it's supposed to work something like this (if done on paper):
For each project, you can have a page with the name of the project, (where the name makes it clear what exactly counts as having finished the project), and a list of actions. Once a week during weekly review, you look at the page for the project, check off any actions you've already done, notice approximately what percentage of the project is already done, think about when you'd like to finish it by, notice which actions can be done now, and copy those actions onto your "next action" lists for the various contexts.
Looking over the project gives you a feel for its priority level in relation to other projects.
The actions listed on the projects page can include actions that can't be done yet because another action has to be done first. After those actions are done, these become "next actions" and can be copied onto the context lists.
After you do an action during the week, you can also immediately write down on your context lists any actions that follow logically from it -- things you couldn't do yet because that had to be done first. If necessary you can consult the project list to find those. However, in case you forget to do this during the week, you can make sure at the next weekly review that the project has at least one "next action" on at least one context list.
A project can have more than one "next action". The "next actions" are all the actions that you can do now. There could be several actions such that it doesn't matter what order you do them in.