SURE vs SEM: which one to use?

Question

in my understanding, SEM should be applied in a case such as: \begin{equation} Y= \alpha_1 + \beta_1 X + \epsilon \end{equation} \begin{equation} X= \alpha_2 + \beta_2 Y + \epsilon \end{equation} as $X$ and $Y$ are jointly determined, while SURE in a case such as: \begin{equation} Y_1= \alpha_1 + \beta_1 X + \epsilon \end{equation} \begin{equation} Y_2= \alpha_2 + \beta_2 X + \epsilon \end{equation} to account for correlation across the error terms of the equations. My question is: I have this case \begin{equation} Y = \alpha_1 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \epsilon \end{equation} \begin{equation} X_1 = \alpha_2 + \beta_4 X_2 + \beta_5 X_4 + \epsilon \end{equation} So we have that $X_1$ and $X_2$ determine $Y$, but $X_2$ determines $X_1$ too. Which method should I use in this case?