atentamente

adv. attentively, thoughtfully, mindfully; sharply; obligingly

adv. mindfully, cautiously

= closely, thoughtfully, attentively.
Ex: Watch closely as the tag number is entered.
Ex: Simenon may be read by many people for amusement only, but if we read him thoughtfully he shows us a variety of insights into the kind of crises that push people into criminal acts.
Ex: The author encourages the reference librarian to listen attentively to children's questions, to be familiar with local school curricula and with currently popular television programmes, films and electronic games.
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* observar atentamente y durante cierto tiempo = maintain + vigil.
* vigilar atentamente = keep + a watchful eye.