Graphs of Sine and Cosine · Challenge problem

The graph of $y=a\sin(bx)+d$, with $a>0$ and $b>0$, passes through $(0,3)$, has maximum value $7$, and reaches its first maximum to the right of the $y$-axis at $x=\dfrac{\pi}{6}$. Find the exact value of $y$ at $x=\dfrac{\pi}{4}$.