Since the release of ChatGPT, large language models (LLMs) have demonstrated remarkable capabilities across various domains. A key challenge in developing these general capabilities is efficiently sourcing diverse, high-quality data. This becomes especially critical in reasoning-related tasks with sandbox checkers, such as math or code, where the goal is to generate correct solutions to specific problems with higher probability. In this work, we introduce Flaming-hot Initiation with Regular Execution (FIRE) sampling, a simple yet highly effective method to efficiently find good responses. Our empirical findings show that FIRE sampling enhances inference-time generation quality and also benefits training in the alignment stage. Furthermore, we explore how FIRE sampling improves performance by promoting diversity and analyze the impact of employing FIRE at different positions within a response.

Autonomous graphical user interface (GUI) agents powered by multimodal large language models have shown great promise. However, a critical yet underexplored issue persists: over-execution, where the agent executes tasks in a fully autonomous way, without adequate assessment of its action confidence to compromise an adaptive human-agent collaboration. This poses substantial risks in complex scenarios, such as those involving ambiguous user instructions, unexpected interruptions, and environmental hijacks. To address the issue, we introduce OS-Kairos, an adaptive GUI agent capable of predicting confidence levels at each interaction step and efficiently deciding whether to act autonomously or seek human intervention. OS-Kairos is developed through two key mechanisms: (i) collaborative probing that annotates confidence scores at each interaction step; (ii) confidence-driven interaction that leverages these confidence scores to elicit the ability of adaptive interaction. Experimental results show that OS-Kairos substantially outperforms existing models on our curated dataset featuring complex scenarios, as well as on established benchmarks such as AITZ and Meta-GUI, with 24.59%~87.29% improvements in task success rate. OS-Kairos facilitates an adaptive human-agent collaboration, prioritizing effectiveness, generality, scalability, and efficiency for real-world GUI interaction. The dataset and codes are available at Anonymous.