Building compliance checking (BCC) is a critical process for ensuring that constructed facilities meet regulatory standards. A core component of BCC is the accurate enumeration of facility types and their spatial distribution. Despite its importance, this problem has been largely overlooked in the literature, posing a significant challenge for BCC and leaving a critical gap in existing workflows. Performing this task manually is time-consuming and labor-intensive. Recent advances in large language models (LLMs) offer new opportunities to enhance automation by combining visual recognition with reasoning capabilities. In this paper, we introduce a new task for BCC: automated facility enumeration, which involves validating the quantity of each facility type against statutory requirements. To address it, we propose a novel method that integrates door detection with LLM-based reasoning. We are the first to apply LLMs to this task and further enhance their performance through a Chain-of-Thought (CoT) pipeline. Our approach generalizes well across diverse datasets and facility types. Experiments on both real-world and synthetic floor plan data demonstrate the effectiveness and robustness of our method.