There are integers \( a \), \( b \), and \( c \), each greater than 1, such that \( \sqrt[a]{N \sqrt[b]{N \sqrt[c]{N}}} = \sqrt[36]{N^{25}} \) for all \( N > 1 \). Find the value of \( b \).

Let's think step by step and output the final answer within \boxed{}.
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