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Ever since the discovery of all-optical magnetization switching (AOS) around a decade ago, this phenomenon of manipulating magnetization using only femtosecond laser pulses has promised a large potential for future data storage and logic devices. Two distinct mechanisms have been observed, where the final magnetization state is either defined by the helicity of many incoming laser pulses, or toggled by a single pulse. What has thus far been elusive, yet essential for applications, is the deterministic writing of a specific magnetization state with a single laser pulse. In this work we experimentally demonstrate such a mechanism by making use of a spin polarized current which is optically generated in a ferromagnetic reference layer, assisting or hindering switching in an adjacent Co/Gd bilayer. We show deterministic writing of an 'up' and 'down' state using a sequence of 1 or 2 pulses, respectively. Moreover, we demonstrate the non-local origin of the effect by varying the magnitude of the generated spin current. Our demonstration of deterministic magnetization writing could provide an essential step towards the implementation of future optically addressable spintronic memory devices.