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I would start by looking at the gears at the end of the axle, and the gears on the wheels them self. All you need to do is remove the wheel to inspect these gears. Also your cable is adjustable so that you can give it more power. Where your cable comes up the handle it is held in place by a pinch type holder. Loosen the bolt and slide the cable down about a half an inch. Normally this takes care of your issue because the cable will stretch over time

There are only two gears inside your transmission. They will not normally wear out. Since you have it open already you should be able to tell just from looking if the gears are in good shape or not. Excessive wear will make the teeth look rounded and non existent