Graphs of Sine and Cosine · Challenge problem

A sinusoid $f(x)=a\sin(bx+c)+d$, with $a>0$ and $b>0$, has period greater than $3$. It satisfies $f(x)+f(x+3)=10$ for every $x$, and it reaches its maximum value $9$ at $x=1$. Find $f(2)$.