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When it comes to a walking/running shoe with good support for your arches you are probably going to need to look at an after market insole that replaces the foot bed that comes with a pair of running shoes. While some footwear has more support than others, when you're looking for solutions for your arches typically the foot bed included with a shoe isn't going to provide much support (which is why they're easily removed). My recommendation would be to schedule an outfitting appointment at your local REI to speak with a footwear expert. They can look at your foot, talk through your needs, and show you the best options available to meet your needs.
I hope this helps, best of luck!
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