Let a, b, and c be complex numbers satisfying the system of equations
\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=9 \\
\frac{a^{2}}{b+c}+\frac{b^{2}}{c+a}+\frac{c^{2}}{a+b}=32 \\
\frac{a^{3}}{b+c}+\frac{b^{3}}{c+a}+\frac{c^{3}}{a+b}=122
Find a b c.