Sec. 3. (a) The court shall not accept a plea of guilty or guilty but mentally ill at the time of the crime without first determining that the plea is voluntary. The court shall determine whether any promises, force, or threats were used to obtain the plea.
(b) The court shall not enter judgment upon a plea of guilty or guilty but mentally ill at the time of the crime unless it is satisfied from its examination of the defendant or the evidence presented that there is a factual basis for the plea.
(c) A plea of guilty or guilty but mentally ill at the time of the crime shall not be deemed to be involuntary under subsection (a) solely because it is the product of an agreement between the prosecution and the defense.