The polynomial \(p(x)\) is given by

\(p(x)=x^3+ax^2-3x+b\),

where \(a\) and \(b\) are constants. The remainder when \(p(x)\) is divided by \(x+3\) is twice the remainder when \(p(x)\) is divided by \(x-2\). It is also given that \(p(x)\) is exactly divisible by \(x+1\). Find the values of \(a\) and \(b\).