Alzheimer's disease (AD) is a growing global health challenge as populations age, and timely, accurate diagnosis is essential to reduce individual and societal burden. However, real-world AD assessment is hampered by incomplete, heterogeneous multimodal data and variability across sites and patient demographics. Although large language models (LLMs) have shown promise in biomedicine, their use in AD has largely been confined to answering narrow, disease-specific questions rather than generating comprehensive diagnostic reports that support clinical decision-making. Here we expand LLM capabilities for clinical decision support by introducing AD-CARE, a modality-agnostic agent that performs guideline-grounded diagnostic assessment from incomplete, heterogeneous inputs without imputing missing modalities. By dynamically orchestrating specialized diagnostic tools and embedding clinical guidelines into LLM-driven reasoning, AD-CARE generates transparent, report-style outputs aligned with real-world clinical workflows. Across six cohorts comprising 10,303 cases, AD-CARE achieved 84.9% diagnostic accuracy, delivering 4.2%-13.7% relative improvements over baseline methods. Despite cohort-level differences, dataset-specific accuracies remain robust (80.4%-98.8%), and the agent consistently outperforms all baselines. AD-CARE reduced performance disparities across racial and age subgroups, decreasing the average dispersion of four metrics by 21%-68% and 28%-51%, respectively. In a controlled reader study, the agent improved neurologist and radiologist accuracy by 6%-11% and more than halved decision time. The framework yielded 2.29%-10.66% absolute gains over eight backbone LLMs and converges their performance. These results show that AD-CARE is a scalable, practically deployable framework that can be integrated into routine clinical workflows for multimodal decision support in AD.

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