A long-video answer is evidence-supported only when the frames decoded from the video cover every event the answer depends on. Existing evaluations score final-answer correctness or predicted evidence intervals, but the frames a method decodes before answering are rarely audited, so correct answers can still rest on incomplete observation. We introduce VES-Bench, a 600-question benchmark of Temporal Ordering and Event Counting items over 348 public long videos. Each item carries a jointly necessary set of evidence intervals, letting us audit at three strictness levels whether a method’s decoded frames cover every one of them. We also propose TRACE, a training-free agent that grounds answers in raw visual clips, builds an evidence bundle round by round, and stops only when the answer stabilises as the bundle grows and a final pass over the same clips returns the same answer. Under a same-backbone audit, TRACE answers 50.7% of questions correctly with at least two decoded frames inside every evidence interval, at 98.7 frames per question: over 10 points above uniform decoding at 128 frames (40.2%), and within 2.6 points of uniform decoding at 256 frames at 0.39× its frame cost, while reaching the highest answer accuracy in the audit (63.5%). TRACE also stays competitive on Video-MME (86.1), LVBench (75.6), and LongVideoBench (75.1).

While Large Language Models (LLMs) have excelled in textual reasoning, they struggle with mathematical domains like geometry that intrinsically rely on visual aids. Existing approaches to Visual Chain-of-Thought (VCoT) are often limited by rigid external tools or fail to generate the high-fidelity, strategically-timed diagrams necessary for complex problem-solving. To bridge this gap, we introduce MathCanvas, a comprehensive framework designed to endow unified Large Multimodal Models (LMMs) with intrinsic VCoT capabilities for mathematics. Our approach consists of two phases. First, a Visual Manipulation stage pre-trains the model on a novel 15.2M-pair corpus, comprising 10M caption-to-diagram pairs (MathCanvas-Imagen) and 5.2M step-by-step editing trajectories (MathCanvas-Edit), to master diagram generation and editing. Second, a Strategic Visual-Aided Reasoning stage fine-tunes the model on MathCanvas-Instruct, a new 219K-example dataset of interleaved visual-textual reasoning paths, teaching it when and how to leverage visual aids. To facilitate rigorous evaluation, we introduce MathCanvas-Bench, a challenging benchmark with 3K problems that require models to produce interleaved visual-textual solutions. Our model, BAGEL-Canvas, trained under this framework, achieves an 86% relative improvement over strong LMM baselines on MathCanvas-Bench, demonstrating excellent generalization to other public math benchmarks. Our work provides a complete toolkit—framework, datasets, and benchmark—to unlock complex, human-like visual reasoning in LMMs.