Enabling Large Language Models (LLMs) to perform tool-free Table Question Answering (TableQA) presents two critical challenges: "question-first" data synthesis often introduces logical hallucinations, while standard reinforcement learning (RL) suffers from sparse rewards over long reasoning chains. We propose ProbeTQA, a unified framework that couples execution-verified data construction with process-supervised RL. To mitigate synthesis hallucinations, ProbeTQA adopts an answer-first executable probing paradigm, in which an agent performs multi-round exploratory programming over real tables so that every synthesized instance is grounded in a verifiable witness program. To address reward sparsity, we convert verified code trajectories into natural-language reasoning traces and derive execution-grounded process rubrics directly from runtime states, providing reliable dense supervision. Using these rubrics, we optimize the model with Group Relative Policy Optimization (GRPO) under a Two-Stage Reward Curriculum, thereby internalizing complex tool-use reasoning into the model parameters. Experiments show that our 8B model achieves state-of-the-art tool-free performance on challenging benchmarks, attaining 65.8% accuracy on TableBench and outperforming GPT-5.4 and DeepSeek-v3.2 by 13.4 and 6.8 percentage points, respectively.

Large language models achieve remarkable performance via extended chain-of-thought (CoT) reasoning, yet this lengthy process incurs substantial inference overhead. Existing CoT compression methods struggle with inflexible manual length budgets, computationally expensive multi-stage training pipelines, and fragile scalability restricted to small models. We propose **HMPO** (**H**ybrid **M**edian-length **P**olicy **O**ptimization), a cost-effective, single-stage reinforcement learning framework. HMPO efficiently compresses CoT via three synergistic components: an *adaptive median-based budget* derived from successful rollouts to eliminate manual tuning, a *cosine-decay token reward* for smooth length penalization, and a *multiplicative reward formulation* that substantially mitigates trivial reward hacking by strictly prioritizing answer correctness. Trained exclusively on mathematical data, HMPO generalizes seamlessly across math, code, science, and instruction-following tasks. Extensive experiments scaling from 9B to 122B parameters across dense and Mixture-of-Experts (MoE) architectures demonstrate that HMPO achieves **19%–46% token compression with negligible accuracy degradation**, all while drastically reducing training costs compared to existing multi-stage baselines.