Two different effects used on one symbol (thing)

Hi,
I need to know how to use two different effects (one after the other) on one symbol. For instance - I have PNG picture with little red square (10x10px). I will import it into KoolMoves (Import Image Graphic) and now, I want that at first step the square will move from left side to the middle, at second step I want to fade it out (Final fade out).
Is it possible to do this with one symbol, or I must add same symbol, put it on the same place as the first symbol and after the first symbol is in the middle I will delete him and put on its place second symbol (with effect of FADE OUT)?

Put the symbol inside a movie clip. Apply one effect to the symbol, the other effect to the movie clip.