Language Reasoning Models (LRMs) achieve strong performance by scaling test-time computation but often suffer from “overthinking”, producing excessively long reasoning traces that increase latency and memory usage. Existing LRMs typically enforce conciseness with uniform length penalties, which over-compress crucial early deduction steps at the sequence level and indiscriminately penalize all queries at the group level. To solve these limitations, we propose PACE, a dual-level framework for prefix-protected and difficulty-aware compression under hierarchical supervision. At the sequence level, prefix-protected optimization employs decaying mixed rollouts to maintain valid reasoning paths while promoting conciseness. At the group level, difficulty-aware penalty dynamically scales length constraints based on query complexity, maintaining exploration for harder questions while curbing redundancy on easier ones. Extensive experiments on DeepSeek-R1-Distill-Qwen (1.5B/7B) demonstrate that PACE achieves a substantial reduction in token usage (up to 55.7%) while simultaneously improving accuracy (up to 4.1%) on math benchmarks, with generalization ability to code, science, and general domains.

While prior work focuses on treating answer verification as a general reasoning or semantic matching problem, significant challenges remain in computation-oriented scientific domains. In this paper, we introduce CoSineVerifier, an agentic verifier that actively invokes external executors to ground its judgments in precise computations and symbolic reasoning. To train this accurate agentic verifier, we propose a novel verifier training data augmentation method to increase the correctness and efficiency of tool-invoked verifications. Extensive experiments across STEM, QA, and long-form reasoning tasks demonstrate CoSineVerifier’s robust generalization abilities, achieving state-of-the-art performance on VerifyBench-Hard and SCI-Bench. Furthermore, when employed as an RLVR reward model, CoSineVerifier consistently outperforms both rubric- and model-based verifiers on AIME’24, AIME’25 and GPQA-D, highlighting its potential to advance LLM reasoning and accelerate data processing