Large Action Models (LAMs) extend large language models by enabling autonomous decision-making and tool execution, making them promising for automating scientific workflows. However, scientific workflows impose strict requirements on reproducibility, auditability, and deterministic execution, which are not satisfied by generic LLM-based agents. Unconstrained action generation can lead to silent state changes, non-deterministic executions, and irreproducible experimental results, limiting the applicability of LAMs in scientific settings. In this paper, we propose R-LAM, a reproducibility-constrained framework for applying Large Action Models to scientific workflow automation. R-LAM introduces structured action schemas, deterministic execution policies, and explicit provenance tracking to ensure that every action and intermediate artifact is auditable and replayable. The framework supports failure-aware execution loops and controlled workflow forking, enabling iterative experimentation without compromising reproducibility. We implement R-LAM as a lightweight Python framework and release it as an open-source PyPI package to facilitate reproducible research. An experimental evaluation of representative scientific workflows demonstrates that R-LAM improves reproducibility success rates and execution reliability compared to unconstrained LLM-based agents, while retaining adaptive control over workflow execution.