## Task A-3.4.

Determine the smallest natural number $n$ for which there exist real numbers $x_{1}, \ldots, x_{n} \in [1,4]$ that satisfy the inequalities:

$$
\begin{aligned}
x_{1}+x_{2}+\ldots+x_{n} & \geqslant \frac{7}{3} n \\
\frac{1}{x_{1}}+\frac{1}{x_{2}}+\ldots+\frac{1}{x_{n}} & \geqslant \frac{2}{3} n
\end{aligned}
$$