A search for non-resonant Higgs boson pair production in the $\mathrm{b\overline{b}}\tau^+\tau^-$ final state is presented. The search is performed using three $\tau\tau$ final states, $e\tau_{\rm h}, \mu\tau_{\rm h}$, and $\tau_{\rm h}\tau_{\rm h}$, where $e$ and $\mu$ indicate a $\tau$ lepton decaying to lighter leptons and $\tau_{\rm h}$ indicates a $\tau$ decay involving hadrons. The analysis uses proton-proton collision data collected in 2016 at 13~\mathrm{TeV} and corresponding to an integrated luminosity of 12.9~\mathrm{fb}^{-1}.

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