Tons of bad advice in this thread. I'm surprised Kean has not already posted here.
Link to Kean's detailing library. OP should read this.
First off, never use Dawn. Its a dish soap designed to strip oil off of whatever it comes in contact with. Including rubber, plastic and door seals.
Second, always remove polish before waxing. The order is Wash, Clay, Wash, Polish, Seal and or Wax. In that order, always, if you go out of order you're not going to get good results.
Finally, clay when done properly strips everything off, including contaminate and left over sealant / wax. Also, clay should always be your first step before you polish, otherwise your polish will pull off the contaminates the clay should be removing and pull it back through your paint, reintroducing the marring you're trying to remove by polishing.