Combine first 6 ingredients in a small bowl, stirring well with a whisk. Place tortillas on a work surface; brush lightly with 2 teaspoons juice mixture. Arrange 1/2 cup lettuce on each tortilla; top each with 3 ounces beef. Combine carrots and mint; arrange about 3 tablespoons carrot mixture over each serving. Drizzle each serving with about 1 tablespoon of remaining juice mixture; roll up.
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