$\vdash\phi \land \diamond\psi \to \diamond(\psi\land\diamond\phi)$ in KB

I’ve been trying to prove $ \vdash\phi \land \diamond\psi \to \diamond(\psi\land\diamond \phi)$ in natural deduction where it’s allowed to use $ \phi\to \square \diamond \phi$ and/or $ \diamond\square\phi\to\phi$ (that is, in $ KB)$ , but I failed. How can one prove this? I’m not including my work because it consists of dozens of pages and doesn’t lead anywhere…