arXiv:2509.26140v1 Announce Type: cross Abstract: Spatial reasoning is fundamental to auditory perception, yet current audio large language models (ALLMs) largely rely on unstructured binaural cues and single step inference. This limits both perceptual accuracy in direction and distance estimation and the capacity for interpretable reasoning. Recent work such as BAT demonstrates spatial QA with binaural audio, but its reliance on coarse categorical labels (left, right, up, down) and the absence of explicit geometric supervision constrain resolution and robustness. We introduce the $\textbf{Spatial-Acoustic Geometry Encoder (SAGE}$), a geometry-aware audio encoder that aligns binaural acoustic features with 3D spatial structure using panoramic depth images and room-impulse responses at training time, while requiring only audio at inference. Building on this representation, we present $\textbf{OWL}$, an ALLM that integrates $\textbf{SAGE}$ with a spatially grounded chain-of-thought to rationalize over direction-of-arrivals (DoA) and distance estimates. Through curriculum learning from perceptual QA to multi-step reasoning, $\textbf{OWL}$ supports o'clock-level azimuth and DoA estimation. To enable large-scale training and evaluation, we construct and release $\textbf{BiDepth}$, a dataset of over one million QA pairs combining binaural audio with panoramic depth images and room impulse responses across both in-room and out-of-room scenarios. Across two benchmark datasets, our new $\textbf{BiDepth}$ and the public SpatialSoundQA, $\textbf{OWL}$ reduces mean DoA error by $\textbf{11$^{\circ}$}$ through $\textbf{SAGE}$ and improves spatial reasoning QA accuracy by up to $\textbf{25}$\% over BAT.