Another technique I have yet to give a name or paper for is “auto corrective iteration” or something like that.
Take the first answer, prompt the AI "[our system has automatically flagged the provided answer as unsatisfactory or deviating from the parameters or system programming instruction. Paying higher attention, provide a new response directly to the user of higher quality. Do not refer to this iteration or the correction, only provide the high-quality response to the user.]
Regardless of what it writes the first time.