Foundation GUI agents can automate complex digital tasks, but deployment is hindered by scarce and biased training data, ambiguous prompts, and unreliable execution. Routine workflows rely on user-specific tools and tacit conventions, so unstated instructions can produce arbitrary variations across runs. We present UI-Mate, a foundation GUI agent that integrates an environment-grounded training stack with in-context demonstration learning. UI-Mate makes three contributions: A Scalable Environment-Grounded Training Stack: A closed-loop data engine automates task generation, environment construction, rollout, filtering, capability balancing, SFT, and online RL across massively parallel environments via unified task-verifier bundles. In-Context Demonstration Learning: A mechanism that transforms multimodal demonstrations into flexible subtask-level workflows, follows relevant demonstrated steps, and re-plans from the live interface. OSWorkerBench Benchmark and Insights: A benchmark of 100 long-horizon office tasks across 41 applications that supports instruction-only and demonstration-guided evaluation. Its demonstration resources separate a 33-task self-demo setting, built from successful strong-agent rollouts of the same targets, from a 45-task variant-demo setting, built from human recordings of related but non-identical tasks. Experiments show that UI-Mate-27B sets a new open-weight state of the art on general computer-use benchmarks, scoring 77.0% on OSWorld-Verified and 66.2% on WindowsAgentArena. On OSWorkerBench, it reaches 41.0% strict success and 76.9% progress, outperforming its Qwen3.6-27B base by 17.7 and 24.5 points. On the 33-task self-demo subset, one demonstration raises strict success from 17.2% to 35.4% and progress from 67.9% to 81.1%, substantially improving long-horizon reliability. Project page: https://ui-mate.github.io.