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A key issue is that current systems fail to incorporate the rich contextual information necessary to resolve ambiguities and omitted details, resulting in literal, inappropriate, or misaligned translations. In this work, we present a framework to improve large language model-based translation systems by incorporating contextual information in bilingual conversational settings during training and inference. We validate our proposed framework on two task-oriented domains: customer chat and user-assistant interaction. Across both settings, the system produced by our framework\u2014TowerChat\u2014consistently results in better translations than state-of-the-art systems like GPT-4o and TowerInstruct, as measured by multiple automatic translation quality metrics on several language pairs. 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