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For kinetics you should be looking at how the reaction is progressing by looking at the rates and the actual pathway of the reaction. For thermodynamics you should be looking at the initial and final rates and making sure you understand the energies involved with both of them.
I think a better mindset to have when considering a reaction is to think that thermodynamic analysis tells us whether the forward or reverse reaction is favored (spontaneous or not spontaneous). However, thermodynamics does not tell us about the pathway, which is where kinetics comes in. From kinetics we can tell the speed or rate of a reaction and look into different mechanisms that factor into different reactions.
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