What the group is good at in your second category is precisely defining the shape of the problem. In my experience the solution is then still born from an indiv

What the group is good at in your second category is precisely defining the shape of the problem. In my experience the solution is then still born from an individual's creative efforts, even during this group effort. I prefer the sandwich model of cooperation: get together to define the problem, separate to work on it, get together to review solutions, iterate.