Final answer:
The client's actions, aiming to control diabetes through diet and exercise and seeking educational resources, align with the Health Belief Model. This model involves personal beliefs about health conditions and behaviors that can prevent or manage health issues.
Step-by-step explanation:
The actions of the client who is recently diagnosed with diabetes mellitus and believes blood sugar control can be improved with diet and exercise are most representative of the Health Belief Model. This model relates to an individual's perception of the threat of a health problem and the accompanying appraisal of the recommended behavior for preventing or managing the problem. The client's decision to utilize resources such as a video on the management of diabetes at the HMO education center indicates an engagement in self-education, which is a proactive step in managing personal health, indicative of the Health Belief Model.