Final answer:
Poison control staff might not recommend giving syrup of ipecac, as the practice of inducing vomiting is generally not advised in cases of poisoning.
Step-by-step explanation:
The question asks which action poison control staff might NOT encourage after someone has been exposed to a poison. While observing the patient, drinking milk, or drinking water might be recommended in certain situations, giving syrup of ipecac is generally NOT recommended. Syrup of ipecac was once used to induce vomiting in cases of poisoning, but this practice has fallen out of favor due to potential complications and the realization that immediate vomiting is not always helpful, and can sometimes worsen the situation. It's important for anyone dealing with a potential poisoning to contact poison control or seek medical advice for instructions specific to the substance involved.