To prepare the reduction, heat vinegar, sugar, and strawberries in a 2-qt stockpot until boiling. Reduce the heat to medium-low and cook until the mixture thickens (it will reduce by about half). Strain and let the mixture cool.
To assemble the salad, place the first 6 ingredients in a large salad bowl. Add olive oil and balsamic reduction and sprinkle with salt and pepper. Toss gently until the greens are fully coated with the dressing.
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