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?