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Integrated Circuit (IC) verification consumes nearly 70% of the IC development cycle, and recent research leverages Large Language Models (LLMs) to automatically generate testbenches and reduce verification overhead. However, LLMs have difficulty generating testbenches correctly. Unlike high-level programming languages, Hardware Description Languages (HDLs) are extremely rare in LLMs training data, leading LLMs to produce incorrect code. To overcome challenges when using LLMs to generate Universal Verification Methodology (UVM) testbenches and sequences, wepropose HAVEN (Hybrid Automated Verification ENgine) to prevent LLMs from writing HDL directly. For UVM testbench generation, HAVEN utilizes LLM agents to analyze design specifications to produce a structured architectural plan. The HAVEN Template Engine then combines with predefined and protocol-specific templates to generate all UVM components with correct bus-handshake timing. For UVM sequence generation, HAVEN introduces a Protocol-Aware Sequence Domain-Specific Language (DSL) that decomposes sequences into fine-grained step types. A set of predefined DSL patterns first establishes sequences that achieve a high coverage rate without LLM involvement. HAVEN continues to improve the coverage rate by iteratively leveraging LLM agents to analyze coverage gap reports and compose additional targeted DSL sequences. Unlike previous works, HAVEN is the first system that utilizes pre-defined, protocol-specific Jinja2 templates to generate all UVM components and UVM sequences using our proposed Protocol-Aware DSL and rule-based code generator. Our experimental results on 19 open-source IP designs spanning three interface protocols (Direct, Wishbone, AXI4-Lite) show that HAVEN achieves 100% compilation success, 90.6% code coverage, and 87.9% functional coverage on average, and is SOTA among LLM-assisted testbench generation systems.