Which research methods come first in a design process? I recommend focusing first on Learn, Look, Ask research methods rather than Try categories.
It nearly always makes sense to focus on evaluating an existing situation first, before proposing solutions to problems or for things which have not yet been documented or captured. Whether it is done consciously, deliberately, or not, the first step in design action involves researching and evaluating existing AS-IS situations prior to creating new designs.
There is always a prior context that can be understood, described, tested and evaluated, that we can learn from to inform a future design. We call this the situation, case, or context. Only after gathering data from an existing AS-IS situation should we think about creating a mock-up or trying new solutions. After all what is the solution solving? In any case a mock-up will be based on or refer to an understanding (analysis of the data) of the current case, an existing context, a prior or existing situation.
Consequently: we should first understand the needs, find the problem(s), before commencing a series of iterative end-to-end design processes. Recall the IDEO Shopping Cart. With the shopping cart as their context the IDEO team first set out to understand (variously) the AS-IS of contemporary shopping carts: their actual use, how they perform, the value/utility offered by them, the problems associated with them, areas to improve...
Productive design action is intimately linked with a motivating `brief'. A brief is a statement of `needs' justified by `evidence'. They are insightful analyses of primary research, research data produced by users, recorded by researchers. A brief should not specify the design. Design briefs are open-ended descriptions that initiate design action, where design action can be understood as deliberate (although sometimes accidental) change in the world. Any design brief should conceivably be addressed perfectly well by a range of possible design solutions.
The design brief is a great place to start but who comes up with the initial design brief? What goes into it? The DT2 research project addresses these questions. It is a platform for you to understand (and perform) the beginning of a design process, what goes into producing useful, actionable initial design briefs.