Analog/mixed-signal circuits are key for interfacing electronics with the physical world. Their design, however, remains a largely handcrafted process, resulting in long and error-prone design cycles. While the recent rise of AI-based reinforcement learning and generative AI has created new techniques to automate this task, the need for many time-consuming simulations is a critical bottleneck hindering the overall efficiency. Furthermore, the lack of explainability of the resulting design solutions hampers widespread adoption of the tools. To address these issues, a novel agentic AI framework for sample-efficient and explainable analog circuit sizing is presented. It employs a multi-agent workflow where specialized Large Language Model (LLM)-based agents collaborate to interpret the circuit topology, to understand the design goals, and to iteratively refine the circuit's design parameters towards the target goals with human-interpretable reasoning. The adaptive simulation strategy creates an intelligent control that yields a high sample efficiency. The AnaFlow framework is demonstrated for two circuits of varying complexity and is able to complete the sizing task fully automatically, differently from pure Bayesian optimization and reinforcement learning approaches. The system learns from its optimization history to avoid past mistakes and to accelerate convergence. The inherent explainability makes this a powerful tool for analog design space exploration and a new paradigm in analog EDA, where AI agents serve as transparent design assistants.