The policy rationale underlying the waiver doctrine is that "it is both unfair and inefficient to permit a claim of error on appeal that, if timely brought to the attention of the trial court, could have been easily corrected or avoided." (People v. Vera (1997) 15 Cal.4th 269, 276.) "Counsel is charged with understanding, advocating, and clarifying permissible sentencing choices at the hearing. Routine defects in the court's statement of reasons are easily prevented and corrected if called to the court's attention." (People v. Scott (1994) 9 Cal.4th 331, 353 (Scott).) Furthermore, if the sentence that the trial court imposed is indeed "unauthorized," then the failure to object does not waive the error. (Scott, supra, 9 Cal.4th at p. 354.) The California Supreme Court has explained that an " 'unauthorized sentence' " is one that "could not lawfully be imposed under any circumstance in the particular case. Appellate courts are willing to intervene in the first instance because such error is 'clear and correctable' independent of any factual issues presented by the record at sentencing." (Ibid.) It is also the rule: " 'A law established for a public reason cannot be waived or circumvented by a private act or agreement.' " (Bickel v. City of Piedmont (1997) 16 Cal.4th 1040, 1048.) "Even less should a party's inaction waive a statutory requirement established for the public benefit." (People v. Bonnetta (2009) 46 Cal.4th 143, 153.)