Einstein Equivalence Principle (EEP) states that
A frame linearly accelerated relative to an inertial frame in special relativity is LOCALLY identical to a frame at rest in a gravitational field.
And also, from this answer, it is stated that the EEP leads to the deduction that a test particle shall follow geodesic.
The reason that the equivalence principle is central to GR is in the fact that you can represent the gravitational field with a metric tensor at all--you can replace a force equation with a geodesic equation for a test mass precisely due to the fact that the geodesic that that test mass follows (or the "acceleration" felt by a Newtonian mass) is independent of the mass of that test particle.
But I fail to see how to infer logically from Einstein Equivalence Principle that a test particle should follow geodesic. Any ideas?