Final answer:
The priority action for a client with diabetes reporting dizziness, weakness, and shakiness is to assess their blood glucose level to determine if they are experiencing hypoglycemia before considering other interventions.
Step-by-step explanation:
If a client with diabetes mellitus reports feeling dizzy, weak, and shaky, the priority action by the nurse would be to assess the client's blood glucose level. These symptoms could indicate hypoglycemia, a state of low blood sugar. Administering insulin, as suggested in options (a) and (c), would be inappropriate without first confirming the blood glucose level since insulin decreases blood glucose levels. Option (b) may be necessary if hypoglycemia is confirmed, but it should not be provided before assessment. Encouraging the client to exercise, option (c), is not the priority, as it could further lower glucose levels and exacerbate the condition. Therefore, the correct response is to first assess the blood sugar level.