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1
Preheat oven to 350 degrees F (175 degrees C). Spray a casserole dish with cooking spray.
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2
Fill a large pot with lightly salted water and bring to a rolling boil. Stir in the fettuccine, bring back to a boil, and cook pasta over medium heat until cooked through but still firm to the bite, about 8 minutes. Drain.
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3
Heat olive oil in a skillet over medium heat; cook and stir chicken strips in the hot oil until no longer pink, about 10 minutes. Remove chicken to a bowl, leaving pan drippings in skillet. Melt margarine in the hot skillet; cook and stir mushrooms, onion, and garlic in skillet until mushrooms have softened and given up their liquid, about 5 minutes. Stir red bell pepper into mixture and sprinkle with flour. Stir to coat and cook, stirring constantly, for 1 minute.
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4
Slowly mix chicken broth into vegetables, stirring to form a thick sauce; mix cream and milk into sauce. Simmer until thickened, about 1 minute. Mix 1/2 cup Swiss cheese, 1/2 cup Cheddar cheese, 1/4 cup Parmesan cheese, thyme, salt, and black pepper into sauce and simmer until cheese have melted and combined with sauce.
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5
Spread half the cooked fettuccine pasta into bottom of prepared casserole dish, top with half the chicken and half the cream sauce. Repeat layers once more and sprinkle remaining 2 tablespoons Swiss cheese, 2 tablespoons Cheddar cheese, and 2 tablespoons Parmesan cheese over the top.
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6
Bake in the preheated oven until cheese topping is nicely browned, 25 to 30 minutes.
