Does a sentencing court need to state facts, not reasons, but merely reasons?

In making a sentence choice under Penal Code section 1170, subdivision (c) (and consequently under rule 406(b)), the sentencing court need not state facts, but merely reasons. (See People v. Prothro (1989) 215 Cal.App.3d 166, 170-171, 263 Cal.Rptr. 433; People v. Golliver (1990) 219 Cal.App.3d 1612, 1617, 1620, 269 Cal.Rptr. 191.) "[S]o long as the record discloses facts which adequately support those reasons, the trial court's choice will be presumed to have been made on the basis of those facts...." (Id. at p. 1620, 269 Cal.Rptr. 191.) The presumption is rebuttable. (At p. 1621, fn. 6, 269 Cal.Rptr. 191.)