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The decays D → K−π+π+π− and D → K−π+π 0 are studied in a sample of quantum-correlated DD¯ pairs produced through the process e+e− → ψ(3770) → DD¯, exploiting a data set collected by the BESIII experiment that corresponds to an integrated luminosity of 2.93 fb−1 . Here D indicates a quantum superposition of a D0 and a D¯ 0 meson. By reconstructing one neutral charm meson in a signal decay, and the other in the same or a different final state, observables are measured that contain information on the coherence factors and average strong-phase differences of each of the signal modes. These parameters are critical inputs in the measurement of the angle γ of the Unitarity Triangle in B− → DK− decays at the LHCb and Belle II experiments. The coherence factors are determined to be RK3π = 0.52+0.12−0.10 and RKππ0 = 0.78 ± 0.04, with values for the average strong-phase differences that are δ K3π D = (167+31−19)◦ and δKππ0D = (196+14−15◦ , where the uncertainties include both statistical and systematic contributions. The analysis is re-performed in four bins of the phase-space of the D → K−π+π+π− to yield results that will allow for a more sensitive measurement of γ with this mode, to which the BESIII inputs will contribute an uncertainty of around 6◦.