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“absentmindedly”
absentmindedly (adverb); more absentmindedly, most absentmindedly
Pertaining to how, in a preoccupied manner, the object of focus is diverted by irrelevant thoughts or some environmental events: Today Alice absentmindedly put orange juice into her breakfast coffee.
Jesse, the scientist, appeared to be puttering around in his garden absentmindedly, but he was really distracted because he was thinking about a new scientific formula.