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Process blackberries in a blender until smooth, stopping to scrape down sides.
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Pour through a fine wire-mesh strainer into a medium saucepan, discarding solids.
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Stir in remaining ingredients; bring mixture to a boil over medium heat, stirring occasionally.
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Boil, stirring occasionally, 1 minute.
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Remove from heat; cool.
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Serve with cobbler, pound cake, fruit, pancakes, or ice cream.