I'm trying to answer a question, one part of which asks me to provide either an informal semantic argument or a counterexample to determine whether $(\lozenge\phi\wedge\lozenge\psi) \rightarrow (\lozenge(\phi\wedge\lozenge\psi)\vee\lozenge(\psi\wedge\lozenge\phi))$ is a valid formula in system K.
It then asks me, for those parts of the question I've found to be false, to determine what conditions I can impose on the accessibility relation in order to make it valid.
I haven't been able to come up with either a proof or a counterexample, so I'd really appreciate any help you could offer. If it turns out that it isn't valid, then some sort of hint for what conditions are necessary would be really helpful too. Thanks!