Find the unique value of $a$ for which the polynomial $x^3 - 12x^2 + ax - 64$ has all real, nonnegative roots.
<|im_start|>system
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<|im_start|>user
Find the unique value of $a$ for which the polynomial $x^3 - 12x^2 + ax - 64$ has all real, nonnegative roots.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
48
Find the unique value of $a$ for which the polynomial $x^3 - 12x^2 + ax - 64$ has all real, nonnegative roots.
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