The average of twelve numbers is 55.5. The average of the first four numbers is 53.4 and that of the next four numbers is 54.6. The $$10^{th}$$ number is greater than the $$9^{th}$$ number by 3 but lesser than the $$11^{th}$$ and $$12^{th}$$ numbers by 2 and 3, respectively. What is the average of the $$10^{th}$$ and the $$12^{th}$$ numbers ?
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