Suppose the curve $y = x^4+ a x^3 + b x^2 +c x +d$ has a tangent line when $x = 0$ with equation $y = 3 x+1$ and a tangent line when $x = 1$ with equation $y = 3x-1.$ Find the values of $a,$ $b,$ $c,$ and $d.$

Answer: $a =$ , $b =$ , $c =$ , and $d =$

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