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Yep, both things you said are right. The standard reduction potential for Br2 is 1.07 V and for I2 it is 0.54V. So Br2 has a greater tendency to get reduced, meaning it has a lower reducing power since it is worse at reducing other species, and it has a stronger oxidizing power since it has a higher reduction potential so it is more likely to oxidize other species.
For these kinds of problems, use the chart for standard reduction potentials. The larger (more positive) the standard potential, the easier it is to be reduced. The species that is reduced is also the oxidizing agent. Hope this helps!
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