In recent years, there has been growing interest in agents that collaborate with humans on creative tasks, and research has begun to explore such collaboration within Minecraft. However, most existing studies on agents in Minecraft focus on scenarios where an agent constructs objects independently on the basis of given instructions, making it difficult to achieve joint construction through dialogue-based cooperation with humans. Prior work, such as the Action-Utterance Model, used small-scale large language models (LLMs), which resulted in limited accuracy. In this study, we attempt to build an agent capable of collaborative construction using LLMs by integrating the framework of the Action-Utterance Model with that of Creative Agents, which leverages more recent and powerful LLMs for more accurate and flexible building. We had two agents conduct the Collaborative Garden Task through simulations and evaluate both the generated gardens and the dialogue content. Through this evaluation, we confirm that the agents are capable of producing gardens with a certain level of quality and can actively offer suggestions and assert their opinions. Furthermore, we conduct a comparative analysis with human-human collaboration to identify current challenges faced by agents and to discuss future directions for improvement toward achieving more human-like cooperative behavior.