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Relying on a single large model to perform end-to-end reasoning and prediction often incurs substantial inference cost. In contrast, DUET decomposes inference into two stages: the capable model produces a reasoning signal, and the lightweight model interprets this signal to generate the final answer, allowing reasoning-intensive computation to be handled by the capable model while non-reasoning-intensive components are delegated to the lightweight model without sacrificing task performance. To achieve this objective, we propose a length-penalized joint training objective that encourages the capable model to transmit only the information that is sufficient for the lightweight model to solve the task. 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