Security vulnerabilities in Internet-of-Things devices, mobile platforms, and autonomous systems remain critical. Traditional mutation-based fuzzers -- while effectively explore code paths -- primarily perform byte- or bit-level edits without semantic reasoning. Coverage-guided tools such as AFL++ use dictionaries, grammars, and splicing heuristics to impose shallow structural constraints, leaving deeper protocol logic, inter-field dependencies, and domain-specific semantics unaddressed. Conversely, reasoning-capable large language models (LLMs) can leverage pretraining knowledge to understand input formats, respect complex constraints, and propose targeted mutations, much like an experienced reverse engineer or testing expert. However, lacking ground truth for "correct" mutation reasoning makes supervised fine-tuning impractical, motivating explorations of off-the-shelf LLMs via prompt-based few-shot learning. To bridge this gap, we present an open-source microservices framework that integrates reasoning LLMs with AFL++ on Google's FuzzBench, tackling asynchronous execution and divergent hardware demands (GPU- vs. CPU-intensive) of LLMs and fuzzers. We evaluate four research questions: (R1) How can reasoning LLMs be integrated into the fuzzing mutation loop? (R2) Do few-shot prompts yield higher-quality mutations than zero-shot? (R3) Can prompt engineering with off-the-shelf models improve fuzzing directly? and (R4) Which open-source reasoning LLMs perform best under prompt-only conditions? Experiments with Llama3.3, Deepseek-r1-Distill-Llama-70B, QwQ-32B, and Gemma3 highlight Deepseek as the most promising. Mutation effectiveness depends more on prompt complexity and model choice than shot count. Response latency and throughput bottlenecks remain key obstacles, offering directions for future work.