While audio large language models have achieved remarkable progress in auditory perception, they still lag behind text-based large language models in deep logical reasoning capabilities. This performance disparity primarily stems from the scarcity of high-quality audio reasoning data. To bridge this modality gap, we propose a novel cross-modal on-policy distillation framework. Our approach leverages a powerful text model as a teacher to provide dynamic correction and guidance to the audio foundational model during on-policy exploration. Furthermore, we construct a three-tier symmetric dataset encompassing logical reasoning, complex audio reasoning, and speech dialogue. By dynamically aligning the student model’s reasoning trajectories within the high-noise auditory space with the teacher model’s prior knowledge in the clean text space, our method effectively distills robust reasoning capabilities into the audio domain. Extensive experiments demonstrate that our model achieves substantial improvements on the audio and speech understanding benchmarks, paving a new path for comprehensive audio-language understanding.