Lisa is making fruit baskets for a community event. She plans to make 15 baskets, each containing 12 pieces of fruit. She decides to allocate 2/3 of the fruit in each basket to apples, and then puts 3/5 of the remaining fruit in each basket as oranges, with the rest being bananas. How many pieces of fruit in total are bananas? Let's think step by step and output the final answer within \boxed{}.
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