Task-specific fine-tuning of foundation models is critically dependent on the quality and relevance of the instruction data. While prevailing data selection methods rely exclusively on instruction instances X to approximate the target distribution, we argue that selection should align with the joint distribution of instructions and task-specific labels (X,Y). However, task-specific labels Y are typically unavailable in practice. To address this, we reformulate the task-specific data selection problem and present a novel pipeline that leverages the reasoning capabilities of large language models (LLMs) to infer proxy labels, thereby facilitating joint distribution alignment. Our approach begins by propagating proxy labels from a small target set to a large, unlabeled source corpus. A two-stage filtering process then removes instances with label noise and refines the subset through distribution alignment. This strategy produces more semantically meaningful and task-aware selections than conventional similarity measures based on $X$ alone. Experimental results show that fine-tuning on a subset of only 10K samples, selected from a pool of 300K, achieves performance competitive or superior to state-of-the-art methods. Code is available at https://github.com/tmlr-group/TADS.