끌다 is dragging or pulling, and in these lines the adverb is usually about time: should I drag this bit out, I will not stall on it too long, send your answers while I keep it going like this. It also covers steering something along, as with how Japan intends to take the relationship forward, and grabbing attention, in the slang about pulling aggro hard. Careful with the line about a wildfire, where the verb is really 끄다, to put out or switch off, which looks almost the same.