For a more thorough analysis, here are some suggestions for observation: Do you arms swing away from your body the same distance? When you shift weight to one leg to step does your torso shift evenly? Do your shoulders and hips rotate the same on both sides? What happens if you see an asymmetry and try to correct it?
Our body will do what ever we ask of it, with 600 muscles it can find a way, it can recruit a team to come to work, even if its not the most efficient. The mind seems to have an overwhelming power in this decision making process.