How many base 10 four-digit numbers, $N = \underline{a} \underline{b} \underline{c} \underline{d}$, satisfy all three of the following conditions?

(i) $4000 \leq N < 6000;$  
(ii) $N$ is a multiple of 5;  
(iii) $3 \leq b < c \leq 6$.

Find the number of such numbers.

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