What is the test for determining whether a sentencing court fully understood and properly exercised its discretion?

Defendant argues without authority that the issue of whether the sentencing court fully understood and properly exercised its discretion is a question of law subject to de novo review. As we have determined from the record that the trial court was aware of its discretion to impose less than a de facto LWOP sentence, the only question is whether the trial court abused its discretion. Defendant has not met its burden of clearly showing that the trial court's exercise of its sentencing discretion was irrational or arbitrary. " ' "[T]he burden is on the party attacking the sentence to clearly show that the sentencing decision was irrational or arbitrary. [Citation.] In the absence of such a showing, the trial court is presumed to have acted to achieve legitimate sentencing objectives, and its discretionary determination to impose a particular sentence will not be set aside on review." ' [Citations.] Second, a ' "decision will not be reversed merely because reasonable people might disagree. 'An appellate tribunal is neither authorized nor warranted in substituting its judgment for the judgment of the trial judge' " ' [Citations.] Taken together, these precepts establish that a trial court does not abuse its discretion unless its decision is so irrational or arbitrary that no reasonable person could agree with it." (People v. Carmony (2004) 33 Cal.4th 367, 376-377.)