Large language models (LLMs) demonstrate outstanding capabilities, but challenges remain regarding their ability to solve complex reasoning tasks, as well as their transparency, robustness, truthfulness, and ethical alignment. In this preliminary study, we compile a set of core principles for steering and evaluating the reasoning of LLMs by curating literature from several relevant strands of work: structured reasoning in LLMs, self-evaluation/self-reflection, explainability, AI system safety/security, guidelines for human critical thinking, and ethical/regulatory guidelines for AI. We identify and curate a list of 220 principles from literature, and derive a set of 37 core principles organized into seven categories: assumptions and perspectives, reasoning, information and evidence, robustness and security, ethics, utility, and implications. We conduct a small-scale expert survey, eliciting the subjective importance experts assign to different principles and lay out avenues for future work beyond our preliminary results. We envision that the development of a shared model of principles can serve multiple purposes: monitoring and steering models at inference time, improving model behavior during training, and guiding human evaluation of model reasoning.