A continuous time signal $x(t)=4 \cos(200\pi t)+8 \cos(400\pi t)$, where $t$ is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response $$h(t)=\begin{cases} \frac{2 \sin (300\pi t)}{\pi t},& t\neq 0 \\ 600, & t=0. \end{cases}$$ Let $y(t)$ be the output of this filter. The maximum value of $ \mid y(t) \mid $ is _________.