What high level-skills should one use to solve the problem no matter the context?
It mustn't be the learning objectives; it is a hierarchy of actions that any person will do when solving this problem. You need to figure out these actions from the problem. Be aware of starting to create a list of skills based on which you will afterward make a problem. In such a way, you can end with a problem that does not exist in real life. Again, first, analyse the real-life problem, then the system of skills used for solving it.
Try to create a system, not a list, i.e., show the relations and sequence between the skills. Remember that it is a sketch; you will continue to develop the skill hierarchy in further layers.
Define the subgroups of skills. If your problem is big, then you need this additional step. Probably you have already started to think about how to split it. Here you can improve it by taking into consideration your skill hierarchy. Remember, the skills and the problem are the two sides of the same coin because we use action verbs to describe both. The problem situations: the washer has broken, so I tried to fix it; the angry neighbour came, and I tried to calm him down; the cook cooks to make the visitor happy. So, when one describes the problem, s/he uses the words representing the competency needed to solve it — fix, calm down, cook. Suppose you describe these situations in more detail. In that case, you will see that they demand to use a hierarchy of skills to solve it — from noticing that the washer is broken to analysing how to solve it and finally implementing the chosen strategy of repeating it.