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Understanding the mechanism driving magnetization switching in spin-orbit-torque-assisted devices remains a subject of debate. While originally attributed to the spin Hall effect and spin Rashba-Edelstein effect, recent discoveries related to orbital moments induced by the orbital Hall effect and the orbital Rashba-Edelstein effect have added complexity to the comprehension of the switching process in nonmagnet/ferromagnet bilayers. Addressing this challenge, we present a quantitative investigation of a Pt/Co bilayer by employing atomistic spin dynamics simulations, incorporating the proximity-induced moments of Pt, as well as electrically induced spin and orbital moments obtained from first-principles calculations. Our layer-resolved model elucidates the dampinglike and fieldlike nature of the induced moments by separating them according to their even and odd magnetization dependence. In addition to demonstrating that a larger fieldlike spin-orbit-torque contribution comes from previously disregarded induced orbital moments, our work highlights the necessity of considering interactions with Pt-induced moments at the interface, as they contribute significantly to the switching dynamics.