There is very little difference between the two types of questions that you reference. In one case there is indeed a flaw in the argument but this does not mean that you approach the questions any differently.
I begin all CR questions in the same way (except inference/conclusion and resolve paradox). So whether it is strengthen or weaken or assumption or method or mimic I use a technique that I call "conclusion driven" method or if you prefer the "reverse engineering" method.
This technique begins with an unhurried reading of the stimulus. I like to pause at the end of each sentence and sort of gather myself. Integrate that sentence into the overall stimulus. In this way I arrive at the end of the reading with a good understanding of the scope and the general point of the stimulus. At this point I would not have written anything down.
The key to the whole process is to correctly identify the main conclusion Luckily on the GMAT this often occurs as the last portion of the stimulus. Most of the time the conclusion is at the end of the stimulus. Once you understand the conclusion well, you can ask yourself what evidence you have for that conclusion. The method of reasoning is how the primary evidence relates to the conclusion.
Some examples, maybe the evidence is an analogy to the conclusion, maybe the evidence presents two possible options and excludes one, leaving only the conclusion, maybe the evidence is flawed in that it takes two things that are correlated and calls one of them the cause of the other.
This is what the answer choice to a method of reasoning is all about. How does the evidence relate to the conclusion? This is also the key to strengthen questions, assumption questions, etc. So start these questions in the normal way and the correct answer will be a description of how these relate to each other.
