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Quantum-correlated measurements of the decay $D^{0} \to K^{0}_{\rmS}\pi^{+}\pi^{-}\pi^{0}$ are performed using a data sample corresponding to anintegrated luminosity of 818 pb$^{-1}$ collected at the $\psi(3770)$ resonanceby the CLEO-c detector. Preliminary results are presented for the $CP$-evenfraction $F_{+}$ and the strong-phase differences of this decay. The value of$F_{+}$ is measured to be 0.246 $\pm$ 0.018. The strong-phase differences aremeasured in different regions of $K^{0}_{\rm S}\pi^{+}\pi^{-}\pi^{0}$ phasespace by binning around the intermediate resonances present. The potentialsensitivity of the results for determining the CKM angle $\gamma$ from$B^{\pm}~\to~D(K^{0}_{\mathrm S}\pi^{+}\pi^{-}\pi^{0})K^{\pm}$ decay using thedata collected by the Belle detector is also shown.

Quantum-correlated measurements of $D^{0} \to K^{0}_{\rm S}\pi^{+}\pi^{-}\pi^{0}$ and consequences for the determination of $\gamma$