Minimum of Trig

Level pending

\(a,b\) and \(c\) are positive integers such that the function \[f(x)=a \cos \left(\frac{3}{2}\pi-\frac{x}{c}\right)+b\] satisfies \(f\left(\frac{\pi}{6}\right)=\frac{7}{2}\) and has a minimum value of \(-3\). What is the value of \(a+b+c\)?

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