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Consider an LTI system with magnitude response $$\mid H(f) \mid=\begin{cases} 1-\frac{\mid f \mid}{20}, & \mid f \mid \leq 20 \\ 0,& \mid f \mid > 20 \end{cases}$$ and phase response $$\arg \{ H(f) \}= – 2f.$$ If the input to the system is $$x(t)=8 \cos \big(20\pi t+\frac{\pi }{4}\big)+16\sin \big(40\pi t+\frac{\pi }{8} \big)+24\cos \big(80\pi t+\frac{\pi }{16} \big),$$ then the average power of the output signal $y(t)$ is ____________