Im a southpaw first and orthodox second, although Im right handed. Since Im right handed my strong hand becomes my lead in southpaw. So for me, its just a matter of making sure my lead hand is stronger than his. Since his lead is his weak hand, it should be easy. If you dont have that then Id work on my footwork and also be sure to try and get to the outside of his lead.
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"When I let Go of who I am, I become who I might be."
Lao Tzu