갈다 is grinding something down — blending chicken and sweet potato into a drink, milling grain, filing your nails — and 넣고 갈다, put it in and blend it, is the shape in several lines. The same verb also means replacing one thing with another, which is where 갈아입다, changing your clothes, comes from. Note the line about filling up with petrol is a different verb that just looks similar in this form.