A system and method of at least partially forming reinforced packages. The method comprises moving a construct in a machine direction on a construct conveyor. The construct conveyor can comprise a primary lug belt with a primary lug, the construct can be disposed on the primary lug belt, and the moving the construct can comprise moving the primary lug belt in the machine direction to push the construct in the machine direction. The method further can comprise positioning a liner on the construct conveyor so that the liner at least partially extends over the construct and moving the liner in the machine direction on a secondary lug belt of the construct conveyor. The secondary lug belt can comprise a secondary lug and the moving the liner can comprise moving the secondary lug belt in the machine direction to push the liner in the machine direction.