The need for contact-rich tasks is rapidly growing in modern manufacturing settings. However, few traditional robotic assembly skills consider environmental constraints during task execution, and most of them use these constraints as termination conditions. In this study, we present a pushing-based hybrid position/force assembly skill that can maximize environmental constraints during task execution. To the best of our knowledge, this is the first work that considers using pushing actions during the execution of the assembly tasks. We have proved that our skill can maximize the utilization of environmental constraints using mobile manipulator system assembly task experiments, and achieve a 100\% success rate in the executions.