GPT-5 without "thinking" mode got the answer wrong.
GPT-5 with thinking answered:
Here are the 21 US states with the letter “R” in their name:
Arizona, Arkansas, California, Colorado, Delaware, Florida, Georgia, Maryland, Missouri, Nebraska, New Hampshire, New Jersey, New York, North Carolina, North Dakota, Oregon, Rhode Island, South Carolina, Vermont, Virginia, West Virginia.
It wrote a script that verified it while doing the "thinking" (feeding the hallusinations back to the LLM)