Two non-decreasing sequences of nonnegative integers have different first terms. Each sequence has the property that each term, beginning with the third, is the sum of the previous term and twice the term before that (i.e., $F_n=F_{n-1}+2F_{n-2}$ for $n\ge 3$). The sixth term of each sequence is $N$. What is the smallest possible value of $N$?