# 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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