Despite the global mental health crisis, access to screenings, professionals, and treatments remains high. In collaboration with licensed psychotherapists, we propose a Conversational AI Therapist with psychotherapeutic Interventions (CaiTI), a platform that leverages large language models (LLM)s and smart devices to enable better mental health self-care. CaiTI can screen the day-to-day functioning using natural and psychotherapeutic conversations. CaiTI leverages reinforcement learning to provide personalized conversation flow. CaiTI can accurately understand and interpret user responses. When the user needs further attention during the conversation, CaiTI can provide conversational psychotherapeutic interventions, including cognitive behavioral therapy (CBT) and motivational interviewing (MI). Leveraging the datasets prepared by the licensed psychotherapists, we experiment and microbenchmark various LLMs' performance in tasks along CaiTI's conversation flow and discuss their strengths and weaknesses. With the psychotherapists, we implement CaiTI and conduct 14-day and 24-week studies. The study results, validated by therapists, demonstrate that CaiTI can converse with users naturally, accurately understand and interpret user responses, and provide psychotherapeutic interventions appropriately and effectively. We showcase the potential of CaiTI LLMs to assist the mental therapy diagnosis and treatment and improve day-to-day functioning screening and precautionary psychotherapeutic intervention systems.