Final answer:
Inform the customer of the health risks associated with undercooked meat, and use a thermometer to verify the temperature of the burger for safety.
Step-by-step explanation:
If a customer insists on a rare burger, the correct action would be to inform the customer that consuming undercooked meat may pose a health risk due to potential bacteria. According to safety guidelines, it is advisable to use a thermometer to ensure food reaches a high enough temperature to kill any bacteria it contains. While the desire to cook the burger to the customer's preferred doneness is understandable, it is the responsibility of the restaurant to prioritize safety.
In addition to verbal communication, many hamburger restaurants have adopted the strategy of maintaining visible kitchen areas to convey to the public that food handling and preparation are conducted in a hygienic and safe manner, thereby reassuring customers of the safety of consuming their products.