Time series analysis is crucial in real-world applications, yet traditional methods focus on isolated tasks only, and recent studies on time series reasoning remain limited to either single-step inference or are constrained to natural language answers. In this work, we introduce TS-Reasoner, a domain-specialized agent designed for multi-step time series inference. By integrating large language model (LLM) reasoning with domain-specific computational tools and an error feedback loop, TS-Reasoner enables domain-informed, constraint-aware analytical workflows that combine symbolic reasoning with precise numerical analysis. We assess the system's capabilities along two axes: (1) fundamental time series understanding assessed by TimeSeriesExam and (2) complex, multi-step inference evaluated by a newly proposed dataset designed to test both compositional reasoning and computational precision in time series analysis. Experiments show that our approach outperforms standalone general-purpose LLMs in both basic time series concept understanding as well as the multi-step time series inference task, highlighting the promise of domain-specialized agents for automating real-world time series reasoning and analysis.