## $\vdash\phi \land \diamond\psi \to \diamond(\psi\land\diamond\phi)$ 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…