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Preheat frying pan with oil over medium heat.Rub salmon on both sides with salt and pepper. Sear until cooked through, 3 to 5 minutes per side; remove from frying pan and set aside.
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Make the avocado spread: stir salt to taste and 1 teaspoon fresh lime juice into the mashed avocados until well combined.
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To assemble sandwiches: spread some of the avocado mixture on each bun and top with a slice of tomato then salmon. Serve with a side of fries or salad.