Final answer:
The nurse should first offer emotional support to the client who is grieving the loss of her hair due to chemotherapy, as this addresses the immediate psychological and emotional needs of the patient.
Step-by-step explanation:
The nurse's first action in response to the client expressing grief over the loss of her hair due to chemotherapy should be to offer emotional support. This approach aligns with person-centered care, acknowledging the patient's emotional and psychological needs. It is important for the nurse to listen and provide compassion and understanding, which can be more immediately necessary than providing practical solutions such as wig catalogs, cold caps, or information on scarves and hats.