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Preheat the oven to 400°F. Cut the chicken breasts across the grain into 1/4-inch-thick slices, toss with lemon juice, and season with salt and pepper. Set aside. Put the potatoes into a medium bowl, season with salt and pepper, sprinkle with 1 tablespoon of the olive oil, and toss. Spread the potatoes in a 13x9-inch baking pan and bake for 10 minutes. Remove from the pan and set aside, covered to keep warm. Put the remaining vegetables into the bowl, sprinkle with 1 tablespoon of olive oil, season with salt and pepper, and toss. Spread the vegetables in the baking pan and bake for 20 minutes, turning about halfway through. Add the remaining 1 tablespoon of olive oil to a hot skillet and saute the chicken pieces until done. Remove from the pan and set aside, covered to keep warm. Combine the tomato paste and 1/3 cup of water in the skillet and cook to reduce to 1/4 cup, scraping up the brown bits from the chicken. Remove the skillet from heat and add the oregano, olives, and chicken. Spread the potatoes and other vegetables on a large platter. Place the chicken/tomato sauce on top and sprinkle with the feta.