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If it's 7-speed, then I will assume it has a freewheel.
I've used 7s Sunrace freewheels with Synchro II levers and it worked really well even for hilly/sporting riding once I put on a 9s Shimano chain. They offer a 13-25t and 13-28t in 7s versions and 13-32t in an 8s version iir.
Note that A and B derailer settings require different indexing rings as the actuation ratio changes.
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