I’d add that one feature of circular reasoning is that it points out beliefs that follow from one another in ways that may not be obvious to some reasoners. If you accept any of the states of the loop as a premise, then the rest of the loop follows. If the logic is valid, then the loop is a package deal. You can’t use it to persuade someone of something, but you can use it to point out cases where when someone’s beliefs are internally inconsistent. This does not tell you whether to accept the whole loop or none of it, of course, but it does suggest you should pick one or the other, unless you can show that it’s not really a logically valid loop.
I’d add that one feature of circular reasoning is that it points out beliefs that follow from one another in ways that may not be obvious to some reasoners. If you accept any of the states of the loop as a premise, then the rest of the loop follows. If the logic is valid, then the loop is a package deal. You can’t use it to persuade someone of something, but you can use it to point out cases where when someone’s beliefs are internally inconsistent. This does not tell you whether to accept the whole loop or none of it, of course, but it does suggest you should pick one or the other, unless you can show that it’s not really a logically valid loop.