I have made a table with the cycles or processes I use and aligned them with Kath Murdoch’s model. We use the cycle that best supports the student's inquiry and leads to ACTION.
Many cycles or processes have elements that are key to a quality inquiry, such as, the traits for writing, or, the elements of music for composition. I find these equally useful.
As inquiry is an active present verb, it is also important to plan for inquiry where students are actively connecting and thinking within the discipline(s). For example, students should not only study scientists and their discoveries, but also experience BEING a scientist to make his or her own discoveries.
In addition there are skills and key questions, even attitudes, that can be used at different stages to support the inquiry. For example, you can use the questions within Problem Solving Talk and Problem Solving Steps for the Math Problem Solving Process. Alternatively, you can use the Question Frames for the Reading Comprehension Cycle.