Proactive robot assistance in household environments requires accurate prediction of human activities and object usage under dynamic and noisy conditions. Existing approaches often rely on complex spatio-temporal models, which can be computationally expensive and sensitive to environmental variability. In this paper, we propose GLOBE, a lightweight framework that combines n-gram Markov models for capturing temporal behavioral patterns with uncertainty-guided large language model (LLM) reasoning. The framework performs sequential prediction efficiently while selectively invoking LLM reasoning only when the model confidence is low. To evaluate performance under realistic conditions, we introduce HOMER-Noise, a noisy extension of the HOMER+ dataset that simulates structured disturbances such as object movements caused by humans, pets, and toddlers. Experimental results show that GLOBE achieves competitive performance with state-of-the-art methods while improving robustness and computational efficiency across both clean and noisy settings. The framework is further validated through a proof-of-concept integration with a Stretch 3 mobile manipulator, demonstrating its potential application in real-world human-robot interaction scenarios.