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Preheat oven to 350°F.
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Pat pork dry and season generously with salt and pepper.
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Sprinkle center of a flameproof roasting pan with 1/2 tablespoon flour.
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Set pork on flour in pan and roast in middle of oven 40 minutes.
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Brush pork with some maple syrup and roast, brushing with maple syrup every 10 minutes, until a thermometer inserted 2 inches into center of meat registers 155°F, 20 to 25 minutes more.
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While pork is roasting, peel potatoes and cut into 1 1/2-inch pieces.
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In a kettle cover potatoes with salted cold water by 2 inches and simmer until tender, about 15 minutes.
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Drain potatoes in a colander set over a large bowl and reserve 3 cups cooking water.
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Return potatoes to kettle and mash with a potato masher, or purée in a food processor.
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Season potatoes with salt and pepper and keep warm.
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Transfer pork to a platter and let stand, loosely covered with foil, 10 minutes.
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While pork is standing, skim fat from pan juices.
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In a small bowl make a beurre manié by kneading together butter and remaining 4 tablespoons flour until smooth.
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Add 1 cup reserved cooking water to roasting pan and deglaze over moderately high heat, stirring and scraping up brown bits.
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Add remaining 2 cups cooking water and any juices that have accumulated on platter and bring mixture to a boil.
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Whisk in beurre manié and simmer sauce, whisking, until thickened to desired consistency, about 2 minutes.
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Pour sauce through a fine sieve into a sauceboat.
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Slice pork and serve with sweet potatoes and sauce.
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Serves 6 to 8.