We develop a method for producing vector sketches one part at a time. To do this, we train a multi-modal language model-based agent using a novel multi-turn process-reward reinforcement learning following supervised fine-tuning. Our approach is enabled by a new dataset we call ControlSketch-Part, containing rich part-level annotations for sketches, obtained using a novel, generic automatic annotation pipeline that segments vector sketches into semantic parts and assigns paths to parts with a structured multi-stage labeling process. Our results indicate that incorporating structured part-level data and providing agent with the visual feedback through the process enables interpretable, controllable, and locally editable text-to-vector sketch generation.