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The sky at MeV energies is currently poorly explored. Here we present an innovative mission concept that builds upon the heritage of past and current missions improving the sensitivity and, very importantly, the angular resolution. This consists in combining a Compton telescope and a coded-mask telescope. We delineate the motivation for such a concept and we define the scientific goals for such a mission. The Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO) is a novel concept for a next-generation telescope covering hard X-ray and soft gamma-ray energies. The potential and importance of this approach that bridges the observational gap in the MeV energy range are presented. With the unprecedented angular resolution of the coded mask telescope combined with the sensitive Compton telescope, a mission such as GECCO can disentangle the discrete sources from the truly diffuse emission. Individual Galactic and extragalactic sources are detected. This also allows to understand the gamma-ray Galactic center excess and the Fermi Bubbles, and to trace the low-energy cosmic rays, and their propagation in the Galaxy. Nuclear and annihilation lines are spatially and spectrally resolved from the continuum emission and from sources, addressing the role of low-energy cosmic rays in star formation and galaxy evolution, the origin of the 511 keV positron line, fundamental physics, and the chemical enrichment in the Galaxy. Such an instrument also detects explosive transient gamma-ray sources, which, in turn, enables identifying and studying the astrophysical objects that produce gravitational waves and neutrinos in a multi-messenger context. By looking at a poorly explored energy band it also allows discoveries of new astrophysical phenomena.