Are the two LTL properties $GF(\psi_1 \land F\psi_2 )$ and $GF(\psi_2 \land F\psi_1 )$ equivalent?

Question

Is $GF(\psi_1 \land F\psi_2 )$ equivalent to the property $GF(\psi_2 \land F\psi_1 )$?

Attempt:

In the first property each state must eventually see $\psi_1$ and $\psi_2$, in the second property as well each state must eventually see $\psi_1$ and $\psi_2$, as such the two properties must be equivalent. Is this correct?