Recent advances in speech large language models (speech LLMs) have enabled seamless spoken interactions, but these systems still struggle with complex reasoning tasks. Previously, chain-of-thought (CoT) prompting or fine-tuning has been to shown to significantly improve the reasoning abilities of text-based LLMs. In this work, we investigate the effect of CoT fine-tuning for multi-stream speech LLMs, demonstrating that reasoning in text space improves the accuracy of speech LLMs by 2.4x, on average, over a suite of spoken reasoning tasks. Beyond accuracy, the latency of the spoken response is a crucial factor for interacting with voice-based agents. Inspired by the human behavior of "thinking while listening," we propose methods to reduce the additional latency from reasoning by allowing the model to start reasoning before the user query has ended. To achieve this, we introduce an entropy-based metric, "question completeness," which acts as an indicator to guide the model on the optimal time to start reasoning. This method provides greater control over the accuracy-latency trade-off compared with heuristic-based approaches and, under equivalent latency conditions, yields a 4% accuracy gain on ARC-Easy. Finally, we use Direct Preference Optimization (DPO) on preference data created using rejection sampling to push the accuracy-latency pareto frontier further, resulting in a 70% reduction in latency without loss in accuracy.