Let $g(x)=\int_0^x f(t) d t$, where $f$ is continuous function in $[0,3]$ such that $\frac{1}{3} \leq f(t) \leq 1$ for all $t \in[0,1]$ and $0 \leq f(t) \leq \frac{1}{2}$ for all $t \in(1,3]$. The largest possible interval in which $g(3)$ lies is :
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