A weird system of equations.

Algebra Level 2

\[\begin{cases} x^{2}+y^{2}+z^{2}=\frac{1}{4} \\\\ x^{3}+y^{3}+z^{3}=\frac{1}{6} \end{cases}\]

How many real solutions \((x, y, z)\) does the system above have?