Sixth-generation (6G) networks are increasingly envisioned as AI-native infrastructures integrating communication, sensing, and computing into a unified fabric. However, existing approaches remain largely optimization-centric, relying on closed-loop control with limited reasoning capability. In this paper, we argue for a paradigm shift toward Agentic AI-Native 6G, in which Large Language Model (LLM)-based agents operate as bounded, policy-governed reasoning entities within a semantic control plane layered above deterministic 3GPP infrastructure. We propose a four-layer architecture that integrates deterministic network infrastructure, semantic abstraction of intent and context, hierarchical reasoning, and a distributed multi-agent fabric spanning device, edge, and core domains. To assess feasibility, we develop a proof-of-concept agentic reasoning and orchestration framework and conduct an extensive empirical study using a domain-specific 6G benchmark under realistic deployment constraints. Our results reveal a fundamental tradeoff between reasoning capability and system efficiency, showing that no single model simultaneously satisfies latency, throughput, and accuracy requirements. Instead, heterogeneous deployment of LLM agents across the device--edge--core continuum is necessary to balance these constraints. We further demonstrate that quantization introduces non-uniform effects across models, reinforcing the need for system-level optimization rather than model-level compression alone. These findings establish agentic intelligence as a viable architectural direction for 6G and highlight key challenges in achieving scalable, trustworthy, and self-reasoning networks. All experimental results and evaluation scripts are publicly available to support reproducibility.