Long-context reasoning remains a critical challenge for Large Language Models (LLMs). Current research typically focuses on curating specialized training data by treating long-context reasoning as a monolithic task, yet it is challenging to verify its quality due to its internal cognitive complexity. In this paper, we propose a paradigm shift: viewing long-context reasoning as a hierarchical spectrum of core atomic skills. To operationalize this, we present an Anchor-based Reasoning (AbR) pipeline that automatically synthesizes strictly verifiable training data for each skill, thereby enabling reliable quality. Diagnostic analyses confirm that proficiency in these atomic skills strongly predicts general long-context reasoning performance. By training exclusively on a highly compact set of merely four thousand synthesized samples with Reinforcement Learning (RL), we explicitly sharpen these foundational capabilities. Extensive experiments across six challenging benchmarks demonstrate that this targeted RL causally delivers robust and generalizable performance gains, outperforming DeepSeek-R1-distill-32B by an average margin of 7.7% (improving from 46.3% to 54.0%). Furthermore, in-depth ablations reveal that these skills operate synergistically, establishing a scalable, data-efficient, and verifiable path to advancing long-context reasoning.