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Geometric magnetic frustration (GMF) has attracted substantial interest due to the exotic physics and rich phase diagrams revealed by the cancellation of normally-dominant magnetic interactions, giving impetus for the search for novel frustrated systems, most often based on antiferromagnetic correlations between magnetic ions decorating triangular or tetrahedral lattices. We report low-temperature magnetic susceptibility and muon spin relaxation results on Li₄MgOsO₆ and Li₃Mg₂OsO₆, members of the A₅BO₆ "rock salt ordered" family of frustrated materials. In Li₃Mg2OsO₆ we find spin freezing below 12K. In Li₄MgOsO₆, which can crystallize into either orthorhombic Fddd or monoclinic C2/m crystal symmetries depending on synthesis conditions, we find magnetism consistent with glassy-like behavior dominating below 2K, with partial ordering and evidence for dynamics at somewhat higher temperatures.