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Both unitary chiral theories and lattice QCD simulations show that the $DK$ interaction is attractive and can form a bound state, namely, $D^*_{s0}(2317)$. Assuming the validity of the heavy antiquark-diquark symmetry (HADS), the $Ξ_{cc}\bar{K}$ interaction is the same as the $DK$ interaction, which implies the existence of a $Ξ_{cc}\bar{K}$ bound state with a binding energy of $49-64$ MeV. In this work, we study whether a $Ξ_{cc}Ξ_{cc}\bar{K}$ three-body system binds. The $Ξ_{cc}Ξ_{cc}$ interaction is described by exchanging $π$, $σ$, $ρ$, and $ω$ mesons, with the corresponding couplings related to those of the $NN$ interaction via the quark model. We indeed find a $Ξ_{cc}Ξ_{cc}\bar{K}$ bound state, with quantum numbers $J^P=0^-$, $I=\frac{1}{2}$, $S=1$ and $C=4$, and a binding energy of $80-118$ MeV. It is interesting to note that this system is very similar to the well-known $NN\bar{K}$ system, which has been studied extensively both theoretically and experimentally. Within the same framework, we show the existence of a $NN\bar{K}$ state with a binding energy of $35-43$ MeV, consistent with the results of other theoretical works and experimental data, which serves as a consistency check on the predicted $Ξ_{cc}Ξ_{cc}\bar{K}$ bound state.