In this paper, we propose a search-augmented large-scale language model (LLM) framework that generates activity chains including household coordination using only publicly accessible statistical and socio-demographic information to address the limitations of existing activity-based models and learning-based human mobility modeling algorithms due to data availability and quality constraints. While existing methods only focus on spatio-temporal patterns, our study enables realistic mobility modeling by considering semantic relationships such as logical connections or dependencies between activities (e.g., household coordination activities such as joint shopping trips or family meal times). The search-augmented mechanism enables household coordination and maintains statistical consistency between the generated patterns. Validation results using NHTS and SCAG-ABM datasets demonstrate effective mobility synthesis and robust adaptability to areas with limited mobility data availability.