Implying correlation of a two random variables from their correlations with a third random variable- $E[YZ]$ given $E[XY]$ and $E[XZ]$

Question

Given we have 1.) $E[XY], E[XZ]$ 2.) $E[X]$, and $E[X^2]$ for all three variables.

Q: How do we arrive at $E[YZ]$?

A follow up $Q:$, if you decide that it is not possible, is that what information is needed to arrive at that number?

Thanks!