4. Let $a$ be a given positive real number, and $n$ be a positive integer greater than 4. Find all $n$-tuples of positive real numbers $\left(x_{1}, x_{2}, \cdots, x_{n}\right)$ that satisfy the system of equations:
$$
\left\{\begin{array}{l}
x_{1} x_{2}\left(3 a-2 x_{3}\right)=a^{3}, \\
x_{2} x_{3}\left(3 a-2 x_{4}\right)=a^{3}, \\
\ldots \ldots \\
x_{n-2} x_{n-1}\left(3 a-2 x_{n}\right)=a^{3}, \\
x_{n-1} x_{n}\left(3 a-2 x_{1}\right)=a^{3}, \\
x_{n} x_{1}\left(3 a-2 x_{2}\right)=a^{3}
\end{array}\right.
$$
Given
$$
x_{i}>0,3 a-2 x_{i}>0(i=1,2, \cdots, n) \text {. }
$$

Notice that,
$$
\begin{aligned}
3 a= & x_{i}+x_{i}+3 a-2 x_{i} \geqslant 3 \sqrt[3]{x_{i}^{2}\left(3 a-2 x_{i}\right)} . \\
& \text { Then } a^{3} \geqslant x_{i}^{2}\left(3 a-2 x_{i}\right)>0 \\
& \Rightarrow \prod_{i=1}^{n} x_{i}^{2}\left(3 a-2 x_{i}\right) \leqslant a^{3 n},
\end{aligned}
$$

The equality holds if and only if $x_{i}=3-2 x_{i}(i=1,2, \cdots, n)$. 
Therefore, the solution to the original system of equations is $(a, a, \cdots, a)$.