Log-based anomaly detection plays a crucial role in ensuring the reliability of systems. While deep learning-based small detection models (SDMs) are efficient, the large language models (LLMs) are accurate and capable of providing explanations. Intuitively, a compelling question arises: Can we seamlessly combine the advantages of both approaches? In this work, we delve into this underexplored research direction and propose CoLA, a novel collaborative log anomaly detection framework. During collaborative inference, an SDM serves as a filter to select potentially anomalous instances, while a downstream LLM acts as an expert to detect anomalies, offer explanations, and refine the SDM. Extensive experiments on three large real-world datasets demonstrate that CoLA significantly outperforms state-of-the-art methods in terms of effectiveness, efficiency, and explainability, while also greatly reducing labor costs.