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 $N \neq 1$. What is the value of $b$?

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