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Two ways that we know that O3 is being reduced is we know that in a redox reaction, one thing must be reduced while the other must be oxidized. We know that the other element in this problem (I don't remember what it was but I remember it was oxidized), was oxidized, so the other substance O3 must have been reduced. The other way of knowing is that if you balance the reduction reaction of O3 --> O2 in either acidic or basic conditions, you'll see that the side with O3 is receiving electrons, which indicates that O3 is the reduced element.
In a redox reaction, there must be both reduction and oxidation, so I would use process of elimination. Also, once you balance out the equation using H+ and H2O, it should be clear which side needs electrons to balance out the charges, and from there you can also decide if it is reduction or oxidation.
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