Stir the canola oil, root beer, Worcestershire sauce, teriyaki sauce, steak sauce, garlic salt, onion salt, black pepper, basil, thyme, and rosemary together in a bowl.
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Remove the steaks from the marinade and shake off excess moisture; discard the remaining marinade. Cook the steaks until they are beginning to firm, and are hot and slightly pink in the center, 5 to 7 minutes per side. An instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C) for medium.
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