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To develop new devices based on synthetic ferrimagnetic heterostructures, understanding the material's physical properties is pivotal. Here, the induced magnetic moment (IMM), magnetic exchange coupling, and spin textures are investigated in Pt(1 nm)/Co(1.5 nm)/Gd(1 nm) multilayers using a multiscale approach. The magnitude and direction of the IMM are interpreted in the framework of both X-ray magnetic circular dichroism and density functional theory. The IMM transferred by Co across the Gd paramagnetic thickness leads to a nontrivial flipped spin state (FSS) within the Gd layers, in which their magnetic moments couple antiparallel/parallel with the ferromagnetic Co near/far from the Co/Gd interface, respectively. The FSS depends on the magnetic field, which, on average, reduces the Gd magnetic moment as the field increases. For the Pt, in both Pt/Co and Gd/Pt interfaces, the IMM follows the same direction as the Co magnetic moment, with negligible IMM in the Gd/Pt interface. Additionally, zero-field spin spirals were imaged using scanning transmission X-ray microscopy, whereas micromagnetic simulations were employed to unfold the interactions, stabilizing the ferrimagnetic configurations, where the existence of a sizable Dzyaloshinskii-Moriya interaction is demonstrated to be crucial.