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I don't think you can use the stoichiometric coefficients from the slow determining step but you can use the reactants and see if what type of molecular reaction it is (i.e. bimolevular, trimolecular, etc.). We use it from the slow-rate determining step because that is the reaction that if it's slow then, the rate will be "determined" by that step, so that's why we look at the slow-step.
Because the slow step kinetically controls the rate of a chemical reaction, the rate law can be determined by looking at the reactants involve in the slow step. That is why we can use the stoichiometric coefficient from slow step to write out the rate law for the whole reaction.
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