This study investigates how Google's Search Generative Experience (SGE), an innovative hybrid search model integrating generative AI summaries with traditional search, impacts user information-searching behaviors. Building on Information Foraging Theory and Cognitive Load Theory, the novel Adaptive Problem Space Construction (APSC) framework conceptualizes how AI-generated content reshapes users' query refinement, cognitive effort, and problem-solving strategies. Utilizing the Type-Aloud Method, a video-based, non-intrusive approach that captures detailed user interactions, this research examines whether SGE promotes deeper cognitive engagement or leads to premature closure by encouraging users to accept synthesized information without further exploration. Results will provide theoretical insights into cognitive adaptation processes in AI-integrated environments and offer empirical evidence on search behaviors influenced by generative AI. Practically, this research informs real-time digital feedback mechanisms, supporting the strategic integration of GenAI and large language models in digital workplaces to enhance innovation, employee performance, and strategic decision-making.