Robotic ultrasound offers advantages over free-hand scanning, including improved reproducibility and reduced operator dependency. In clinical practice, US acquisition relies heavily on the sonographer's experience and situational judgment. When transferring this process to robotic systems, such expertise is often encoded explicitly through fixed procedures and task-specific models, yielding pipelines that can be difficult to adapt to new scanning tasks. In this work, we propose a unified framework for autonomous robotic US scanning that leverages a LLM-based agent to interpret US scanning guidelines and execute scans by dynamically invoking a set of provided software tools. Instead of encoding fixed scanning procedures, the LLM agent retrieves and reasons over guideline steps from scanning handbooks and adapts its planning decisions based on observations and the current scanning state. This enables the system to handle variable and decision-dependent workflows, such as adjusting scanning strategies, repeating steps, or selecting the appropriate next tool call in response to image quality or anatomical findings. Because the reasoning underlying tool selection is also critical for transparent and trustworthy planning, we further fine tune the LLM agent using a RL based strategy to improve both its reasoning quality and the correctness of tool selection and parameterization, while maintaining robust generalization to unseen guidelines and related tasks. We first validate the approach via verbal execution on 10 US scanning guidelines, assessing reasoning as well as tool selection and parameterization, and showing the benefit of RL fine tuning. We then demonstrate real world feasibility on robotic scanning of the gallbladder, spine, and kidney. Overall, the framework follows diverse guidelines and enables reliable autonomous scanning across multiple anatomical targets within a unified system.