The development of Cloud-Edge-IoT applications requires robust programming models. Existing models often struggle to manage the dynamic and stateful nature of these applications effectively. This paper introduces the Collaborative State Machines (CSM) programming model to address these complexities. CSM facilitates the development of reactive, event-driven, and stateful applications targeting the Cloud-Edge-IoT continuum. Applications built with CSM are composed of state machines that collaborate autonomously and can be distributed across different layers of the continuum. Key features of CSM include (i) a sophisticated collaboration mechanism among state machines utilizing events and persistent data; (ii) encapsulation of state through the inherent state of state machines and persistent data; (iii) integration of actions and service invocations within states and state transitions, thereby decoupling complex application logic from compute and data processing services; and (iv) an advanced data model that supports the processing of local, static, and persistent data with defined scope and lifetime. In addition to introducing the CSM programming model, we present a runtime system and a comprehensive evaluation of our approach. This evaluation is based on three use cases: a stress test on a large-scale infrastructure, a surveillance system application, and a complex smart factory scenario, all deployed on the Grid'5000 testbed. Our results demonstrate a 12x increase in throughput through novel language features in the stress test. Compared to Serverless Workflow, a state-of-the-art baseline system, we show a 2.3x improvement in processing time per processed image in a surveillance system use case, a 55x reduction in total processing time for a smart factory use case, and an overall improvement in productivity across these use cases.