I have found the sentence
that was translated as
The study group seemed to have gotten off a good start
But I could not break down "順調に回り", could you explain?
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The third meaning of 回る according to jisho.org is to function well, and 始める is an auxiliary verb which means to start, so 回り始めた means started functioning well.
順調に is the adverb version of 順調, which means favourable, so something like favourably. If you put it all together, 順調に回り始めた is started functioning well favourably. It sounds redundant in English, but if we assume 回る is not as explicit as to function well, and the well is more implicit, the sentence makes sense, and the purpose of 順調に is to emphasize how well it goes.