Real-time voice agents face a tension: end-to-end models often lack deep reasoning, while cascaded ASR–LLM–TTS pipelines achieve stronger reasoning but defer LLM inference until after ASR finalizes the transcript, creating an avoidable post–turn-end silent gap. We target this gap under complex spoken requests that admit a relatively determinate answer, and treat it as system-induced rather than communicatively motivated. Existing cascaded streaming strategies attempt to reduce it via mechanical segmentation (e.g., fixed chunks, VAD-based splitting) or speculative generation, but they frequently either break semantic units or waste computation on predictions that must be rolled back. We propose LTS-VoiceAgent, a Listen–Think–Speak framework that explicitly separates when to think from how to reason incrementally. It features a Dynamic Semantic Trigger to detect meaningful prefixes, and a Dual-Role Stream Orchestrator that coordinates a background Thinker (for state maintenance) and a foreground Speaker (for speculative solving). This parallel design enables "thinking while listening" without committing audible content before turn end. We also introduce a Pause-and-Repair benchmark that injects natural disfluencies as a semantic-level streaming stress test. Experiments across VERA, Spoken-MQA, BigBenchAudio, and our benchmark show that LTS-VoiceAgent achieves a stronger accuracy–latency–efficiency trade-off than serial cascaded baselines and existing streaming strategies.