Let $\{a_n\}_{n\geq 1}$ be an arithmetic sequence and $\{g_n\}_{n\geq 1}$ be a geometric sequence such that the first four terms of $\{a_n+g_n\}$ are $0$, $0$, $1$, and $0$, in that order.  What is the next term of $\{a_n+g_n\}$?

Note: Duplicate problem

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