In a roundabout, indirect, or unnecessarily complex manner; going the long way around.
From circuitous (adjective) plus the adverbial suffix -ly. Circuitous itself comes from circuit through the Latin-derived adjective suffix -ous.
Circuitously is the adverbial form that makes adults sound formal when frustrated: 'Why are you explaining this so circuitously?' It's the fancy way to say someone's taking forever to get to the point.
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