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Heat the oven to 350 degrees.
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Prepare the cake mix according to the instructions on the box, and divide evenly into to well greased 9 inch cake pans. Bake as directed, and allow to cool.
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Prepare the pudding according to the instructions on the box, and chill to set.
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Break one of the cake layers into pieces, and layer in the bottom of a large serving bowl.
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Layer half of the pudding on top of the cake.
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Pour in ½ a can of the pineapple, and spread evenly.
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Add 1 package of strawberries into the serving bowl, followed by one of the sliced bananas.
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Repeat the layers again.
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Spread the Cool Whip topping on top, and chill for several hours up to overnight before serving.