If one particle is dependent on the other how can an action on one particle affect the state of another if when you measure a particle, the result you see is based off of something that technically hasn't happened yet?
Your mistake was thinking each particle has a state. If that were the case they would not be entangled. What happens is you have a joint state for the pair of particles.
Since it starts out a joint state, when you act on the state you act on a joint state so it affects the joint state.
And yes, what we call an observation or a measurement changes the (joint) state (or even the individual state if it has one).