어다

Do it and bring it over

Links one action to a second one that moves the result somewhere or hands it to someone. That is why it appears here glued to 주다 and 놓다: dropping the kids off at school, bringing the food over, bringing coffee, buying something for someone. The first verb says what you do, and the pair together says you then delivered it. It is a fixed piece of words like 가져다주다 (bring), 데려다주다 (drop off) and 사다 주다 (buy for), rather than something you build freely.