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We present results of a study of the decay $J/\psi\rightarrow\omega\eta\pi^+\pi^-$ using a sample of $(225.2\pm2.8)\times10^6$ $J/\psi$ events collected by the BESIII detector, and report the observation of a new process of $J/\psi\rightarrow \omega X(1870)$ in which X(1870) decays to $a_0(980)\pi$. The statistical significance of this process is larger than $7.2\sigma$. …