All-optical helicity-dependent switching in ferromagnetic Co/Pt multilayers is investigated using magneto-optical microscopy and anomalous Hall effect measurements. A state diagram is built by studying the effect of pulse duration, fluence, and spot size. We use numerical solutions of the three-temperature model to explain that the all-optical helicity-dependent switching mechanism relies on the spin bath reaching temperatures close to the Curie point. Further insights into the reversal process are provided by the experimental demonstration of significant helicity-dependent reversal after a single laser pulse that reveals the involvement of direct angular momentum transfer. Moreover, based on the observation that longer pulse durations and larger spot sizes lead to enhanced reversal efficiency, we identify experimental conditions that lead to saturated magnetization reversal after just a few tens of laser pulses.