Step 3: Exclude the incorrect options. For example, FADH$_2$ is the reduced form of FAD and is not directly required in this reaction. ATP, Ubiquinone, Vitamin B$_{12}$, Biotin, Coenzyme Q, Tetrahydrofolate, NADP$^+$, and Pyridoxal phosphate (PLP) are not involved in the pyruvate dehydrogenase complex reaction.