The shortage of mental health professionals has driven the web to become a primary avenue for accessible psychological support. While Large Language Models (LLMs) offer promise for scalable web-based counseling, existing approaches often lack emotional understanding, adaptive strategies, and long-term memory. These limitations pose risks to digital well-being, as disjointed interactions can fail to support vulnerable users effectively. To address these gaps, we introduce TheraMind, a strategic and adaptive agent designed for trustworthy online longitudinal counseling. The cornerstone of TheraMind is a novel dual-loop architecture that decouples the complex counseling process into an Intra-Session Loop for tactical dialogue management and a Cross-Session Loop for strategic therapeutic planning. The Intra-Session Loop perceives the patient's emotional state to dynamically select response strategies while leveraging cross-session memory to ensure continuity. Crucially, the Cross-Session Loop empowers the agent with long-term adaptability by evaluating the efficacy of the applied therapy after each session and adjusting the method for subsequent interactions. We validate our approach in a high-fidelity simulation environment grounded in real clinical cases. Extensive evaluations show that TheraMind outperforms other methods, especially on multi-session metrics like Coherence, Flexibility, and Therapeutic Attunement, validating the effectiveness of its dual-loop design in emulating strategic, adaptive, and longitudinal therapeutic behavior. The code is publicly available at https://github.com/Emo-gml/TheraMind.