Final answer:
The nurse is embodying Gardner's leadership task of motivating and empowering the client, which aligns with option c.
Step-by-step explanation:
The nurse’s actions in relating to and inspiring the client with a psychiatric disorder to achieve client outcomes reflect one of Gardner's leadership tasks. The correct answer is c) Motivating and empowering the client. This task involves the nurse acting as a leader who provides not only care and oversight but also motivation and empowerment to clients, which can help them to manage their conditions more effectively and achieve better health outcomes. Building a cohesive healthcare team, monitoring vital signs and medication, and conducting research on psychiatric disorders are important tasks too but are not directly related to client empowerment.