You're asking abuot something trickier than you think, unless I misunderstand you. Sounds like you're interested in learnign to think in arguments? The first rule of that is that anything anyone says is a claim, whether descriptive, prescriptive or general truth claim. If I say, it's raining out, I'm claiming it's raining out. If I say you're stupid, I'm claiming you're stupid. So, how do you determine what's a convincing argument. Practice.
Alternatively, you may be interested in systems thinking. Google it.
I think I need more details about what sort of things you'd like to apply analytical thinking to. Maybe some examples?
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