Large language models have shown promise for automating data extraction (DE) in systematic reviews (SRs), but most existing approaches require manual interaction. We developed an open-source system using GPT-4o to automatically extract data with no human intervention during the extraction process. We developed the system on a dataset of 290 randomized controlled trials (RCTs) from a published SR about cognitive behavioral therapy for insomnia. We evaluated the system on two other datasets: 5 RCTs from an updated search for the same review and 10 RCTs used in a separate published study that had also evaluated automated DE. We developed the best approach across all variables in the development dataset using GPT-4o. The performance in the updated-search dataset using o3 was 74.9% sensitivity, 76.7% specificity, 75.7 precision, 93.5% variable detection comprehensiveness, and 75.3% accuracy. In both datasets, accuracy was higher for string variables (e.g., country, study design, drug names, and outcome definitions) compared with numeric variables. In the third external validation dataset, GPT-4o showed a lower performance with a mean accuracy of 84.4% compared with the previous study. However, by adjusting our DE method, while maintaining the same prompting technique, we achieved a mean accuracy of 96.3%, which was comparable to the previous manual extraction study. Our system shows potential for assisting the DE of string variables alongside a human reviewer. However, it cannot yet replace humans for numeric DE. Further evaluation across diverse review contexts is needed to establish broader applicability.