Our goal is to build language model based multi-agent systems for complex planning problems involving multiple explicit and implicit constraints, some of which may be commonsense. Our initial investigations reveal that large language models (LLMs) are often unable to maintain consistency across the planning process, whereas large reasoning models (LRMs) struggle with handling implicit commonsense constraints. In response, we introduce LRPlan, a novel domain-independent, language-based multi-agent architecture where LLM and LRM-based agents collaborate at training time to abstract important patterns, heuristics and insights about the domain. At test time, they collaborate in implementing these learned patterns and insights for a new planning instance. We perform experiments on two domains, TravelPlanner and TimeArena-Static, and use two LLM-LRM combinations from GPT and DeepSeek families. We find that LRPlan outperforms various multi-agent and single-agent baselines obtaining notably higher accuracy as well as cost efficiency.