(4) If real numbers $a$, $b$, $c$ satisfy: $a+b+c=a^{2}+b^{2}+c^{2}$, then the maximum value of $a+b+c$ is $\qquad$ .
4 3 Hint: According to the Cauchy-Schwarz inequality,
$$
3(a+b+c)=\left(1^{2}+1^{2}+1^{2}\right)\left(a^{2}+b^{2}+c^{2}\right) \geqslant(a+b+c)^{2},
$$

thus $a+b+c \leqslant 3$, with equality when $a=b=c=1$.