Tosefta for Horayot 24:13

The bull of the anointed [priest] and the bull of the congregation (Hor. 3:6, Hor. 12b:20): the bull of the anointed [priest] precedes the bull of the congregation in all of its actions since the bull of the anointed [priest] atones and the congregation is atoned for. It is better for the one that atones to precede the one that is atoned for, as it says, “To make expiation for himself and for his household” (Lev 16:6). The bull that comes for every mitzvah precedes the bull and goat of idol worship and the bull and goal of idol worship precede the goat of the nasi and the goat of the nasi precedes the goat of the individual and the goat of the individual precedes the ewe of the individual. The two loaves precede the lambs. The omer precedes the lamb offered with it. This is the rule: The one that comes for the sake of the day comes before the one that comes for the sake of the bread.