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Large Language Models (LLMs) have made significant strides in various intelligent tasks but still struggle with complex action reasoning tasks that require systematic search. To address this limitation, we introduce a method that bridges the natural language understanding capability of LLMs with the symbolic reasoning capability of action languages---formal languages for reasoning about actions. Our approach, termed {\sf LLM+AL}, leverages the LLM's strengths in semantic parsing and commonsense knowledge generation alongside the action language's expertise in automated reasoning based on encoded knowledge. We compare {\sf LLM+AL} against state-of-the-art LLMs, including {\sc ChatGPT-4}, {\sc Claude 3 Opus}, {\sc Gemini Ultra 1.0}, and {\sc o1-preview}, using benchmarks for complex reasoning about actions. Our findings indicate that while all methods exhibit various errors, {\sf LLM+AL}, with relatively simple human corrections, consistently leads to correct answers, whereas using LLMs alone does not yield improvements even after human intervention. {\sf LLM+AL} also contributes to automated generation of action languages.