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The decay 𝐽/𝜓→𝛾𝛾𝜙 is studied using a sample of 1.31×109 𝐽/𝜓 events collected with the BESIII detector. Two structures around 1475 MeV/𝑐2 and 1835 MeV/𝑐2 are observed in the 𝛾𝜙 invariant mass spectrum for the first time. With a fit on the 𝛾𝜙 invariant mass, which takes into account the interference between the two structures, and a simple analysis of the angular distribution, the structure around 1475 MeV/𝑐2 is found to favor an assignment as the 𝜂(1475) and the mass and width for the structure around 1835 MeV/𝑐2 are consistent with the 𝑋(1835). The statistical significances of the two structures are 13.5𝜎 and 6.3𝜎, respectively. The results indicate that both 𝜂(1475) and 𝑋(1835) contain a sizeable 𝑠¯𝑠 component.