Lookahead Reasoning-Step Selection (LRSS): Predicting Which Next Reasoning Operation Is Most Likely to Advance the Solution

Large language models solve complex problems through sequences of intermediate reasoning operations. At each stage, a model may choose to continue deriving an answer, decompose the problem, retrieve missing information, perform a calculation, verify an assumption, examine a counterexample, compare alternative explanations, or revise an earlier conclusion. Although these operations can have different consequences for subsequent problem-solving progress, conventional sequential reasoning generally selects the next operation without explicitly estimating the downstream value of alternative reasoning actions. Lookahead Reasoning-Step Selection (LRSS) investigates whether evaluating candidate reasoning operations through short prospective reasoning trajectories can provide useful information for selecting the next operation. Instead of immediately executing the most natural continuation, LRSS generates multiple candidate reasoning operations, constructs limited previews of their possible downstream consequences, and estimates which candidate is most likely to advance the overall solution. The proposed framework consists of five principal components: reasoning-state representation, candidate-operation generation, prospective reasoning expansion, downstream progress estimation, and adaptive operation selection. Candidate operations are evaluated according to their estimated contribution to problem progress, logical validity, uncertainty reduction, information acquisition, and computational cost. A cost-aware selection mechanism is introduced to balance expected reasoning progress against the additional computation required for prospective evaluation. The framework distinguishes immediate plausibility from downstream usefulness. A reasoning operation that appears locally reasonable may fail to resolve an important uncertainty, introduce an unnecessary intermediate step, or lead to an unproductive reasoning direction. Conversely, an operation that initially appears less direct, such as checking an assumption or decomposing a problem, may create a more favorable subsequent reasoning state. This paper presents LRSS as a conceptual and experimentally testable framework for prospective reasoning-operation selection. It defines the mathematical formulation, proposes an implementation procedure, introduces experimental hypotheses, and outlines a controlled evaluation protocol using mathematical reasoning, logical reasoning, and multi-step question-answering tasks. Comparisons with sequential reasoning, confidence-based selection, random operation selection, and tree-based reasoning methods are proposed. No experimental results are claimed in this paper. The central research question is whether short-horizon estimates of downstream reasoning progress can provide useful information beyond the immediate quality or plausibility of a candidate reasoning operation. The proposed framework is intended to support systematic investigation of this question rather than establish an assumed performance advantage.