3. (7p) Solve in $\boldsymbol{R} \times \boldsymbol{R} \times \boldsymbol{R}$ the system:

$$
\left\{\begin{array}{l}
2^{x}+3^{x}=3 y+2 \\
2^{y}+3^{y}=3 z+2 \\
2^{z}+3^{z}=3 x+2
\end{array}\right.
$$

Petru Vlad