A variable circle \(C\) has the equation \(x^2+y^2-2(t^2-3t+1)x-2(t^2+2t)y+t=0\), where\(t\) is a parameter. If the power of the point \(P(a,b)\) with respect to the circle \(C\) is constant then find the ordered pair \((a,b)\).

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