When a team is trying to solve a problem, first thing to do is to select a facilitator, then understand and clarify the problem. Next step is to discuss and list down all possible solutions. Later split into pairs and each pair should explore one option and discuss it again with the team. Select one or two best solutions with team consent. Now, judiciously assign work to each pair. Do not wait for the complete resolution of the problem, instead have shorter iterations followed by discussions.
Once the team reaches the goal, have a retro discussion and everyone should rate the team performance. With every new problem, along with identifying a solution, one should also look at improving self performance score. Make working a learning.