If both sides measure the particle, both sides now know a fact that the other side knows. Let's say that both sides have previously agreed, at sub-light speeds, that "0" will mean "we both sell Microsoft stock" and "1" means "we both buy Microsoft stock". (Assume an entire list of actions so we have more than one bit of common knowledge.) Is this considered a form of FTL communication? Or just a hack?
(also not a physicist, so sorry to any reading this and cringing)
If right before measuring the particle one side gets a new information that e.g. selling the Microsoft stock right now is a really bad idea, they have no way to communicate this information to the other. Both of them will take a synchronized action, but synchronized according to the rules they have agreed on previously. They cannot use entanglement to transmit new information from one side to the other. They can only use it to receive the same random data at the same time, which they can use to take a coordinated action.
So you on one end can measure whether the particle is 0 or 1 and the other person can also do the same, but you cannot alter the state.
Therefore you cannot encode a data stream without an accompanying slower method to transmit by.