Combine the salsa, lime juice, Worcestershire, garlic and 2 tablespoons of the oil in a blender; puree until smooth. Pour into a resealable plastic bag and add the steak pieces. Seal tightly and rub the steaks with the marinade until evenly coated. Set aside for about 30 minutes at room temperature.
Heat the remaining 1 tablespoon oil in a large skillet over medium-high heat. Remove the steaks from the marinade, allowing the excess to drip off. Discard the marinade. Pat the steaks dry with paper towels and season generously with salt and pepper. Lay the steaks in the skillet and cook, turning once, until browned on the outside and medium-rare, 6 to 8 minutes total. Let the steaks rest for 5 minutes. Serve sliced with warm tortillas, sliced avocado, cilantro leaves, lime wedges and extra salsa to make tacos.
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