We evaluated the viability of using Large Language Models (LLMs) to trigger and personalize content in Just-in-Time Adaptive Interventions (JITAIs) in digital health. As an interaction pattern representative of context-aware computing, JITAIs are being explored for their potential to support sustainable behavior change, adapting interventions to an individual's current context and needs. Challenging traditional JITAI implementation models, which face severe scalability and flexibility limitations, we tested GPT-4 for suggesting JITAIs in the use case of heart-healthy activity in cardiac rehabilitation. Using three personas representing patients affected by CVD with varying severeness and five context sets per persona, we generated 450 JITAI decisions and messages. These were systematically evaluated against those created by 10 laypersons (LayPs) and 10 healthcare professionals (HCPs). GPT-4-generated JITAIs surpassed human-generated intervention suggestions, outperforming both LayPs and HCPs across all metrics (i.e., appropriateness, engagement, effectiveness, and professionalism). These results highlight the potential of LLMs to enhance JITAI implementations in personalized health interventions, demonstrating how generative AI could revolutionize context-aware computing.