Given that the polynomial \(x^3 + 2x^2 - 5x + 6 = 0\) has roots \(a\), \(b\), and \(c\), and that the polynomial \(x^3 + px^2 + qx + r = 0\) has roots \(a+b\), \(b+c\), and \(c+a\), determine the value of \(r\). Let's think step by step and output the final answer within \boxed{}.
user