3. Let $f=uv\left(u, v \in \mathbf{R}_{+}\right)$. It is known that for all positive triples $(a, b, c)$ satisfying $a+b+c=1$, the inequality
$$
u(ab+bc+ca)+vabc \leqslant \frac{7}{3}
$$

always holds. Then the maximum value of $f$ is . $\qquad$