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There are many Root Cause Analysis techniques available to find the root cause of a problem and to find the appropriate solution.
Here the important point is to know your problem, do the RCA put the corrective and preventive actions and avoid jumping directly to the solution without proper RCA.
The other important point is think beyond the fix to ensure the same or similar kind of problem will not occur in future.
Most problems have multiple solutions, some we have to be very precise an focus more on the outcome as a solution. Working together as a team and brain storming ideas will definitely lead us to the best solution possible. Solutions arise from experiences, manuals and knowledge.