Foundation models provide the adaptability needed in robotics but often require explicit tasks or human verification due to potential unreliability in their responses, complicating human-robot collaboration (HRC). To enhance the reliability of such task-planning systems, we propose 1) an adaptive task-planning system for HRC that reliably performs non-predefined tasks implicitly instructed through HRC, and 2) an integrated system combining multimodal large language model (LLM)-based task planning with multimodal communication of human intention to increase the HRC success rate and comfort. The proposed system integrates GPT-4V for adaptive task planning and comprehension evaluation during HRC with multimodal communication of human intention through speech and deictic gestures. Four pick-and-place tasks of gradually increasing difficulty were used in three experiments, each evaluating a key aspect of the proposed system: task planning, comprehension evaluation, and multimodal communication. The quantitative results show that the proposed system can interpret implicitly instructed tabletop pick-and-place tasks through HRC, providing the next object to pick and the correct position to place it, achieving a mean success rate of 0.80. Additionally, the system can evaluate its comprehension of three of the four tasks with an average precision of 0.87. The qualitative results show that multimodal communication not only significantly enhances the success rate but also the feelings of trust and control, willingness to use again, and sense of collaboration during HRC.