Plan-and-Solve Prompting: A Better Zero-Shot Alternative to Let's Think Step by Step

Zero-Shot Chain-of-Thought prompting, introduced by Kojima et al. in 2022, showed that appending 'Let's think step by step' to a question produces step-by-step reasoning from large language models without any hand-written demonstrations. The approach was surprisingly effective, but the trigger sentence is blunt: it tells the model to reason without specifying what that reasoning should look like. A closer inspection of errors reveals the gaps. Among 100 GSM8K math problems sampled from GPT-3 (text-davinci-003) outputs, 46 were answered incorrectly. Of those, 7 had calculation errors, 12 had missing-step errors where a required intermediate step was skipped, and 27 had semantic misunderstanding errors where the model misread the problem or produced an incoherent reasoning chain. Plan-and-Solve (PS) Prompting, published at ACL 2023 (arXiv:2305.04091) by Lei Wang, Wanyu Xu, Yihuai Lan, Zhiqiang Hu, Yunshi Lan, Roy Ka-Wei Lee, and Ee-Peng Lim from Singapore Management University, Singapore University of Technology and Design, Southwest Jiaotong University, and East China Normal University, replaces that single trigger with a two-part instruction that explicitly asks the model to plan first and then execute.

Three failure modes that motivated the method

The paper's error taxonomy gives each failure mode a distinct cause. Calculation errors arise when the model sets up the right reasoning path but computes a wrong intermediate value. Missing-step errors occur when the model skips a required step, often because 'Let's think step by step' does not specify what steps are needed or how many. Semantic misunderstanding errors are the largest category: the model misidentifies what the question is asking, or its generated steps lose coherence partway through. Zero-Shot-CoT addresses none of these directly. The trigger 'Let's think step by step' elicits some structure but provides no mechanism for the model to audit whether its plan covers all necessary steps or whether its arithmetic is correct. PS prompting addresses missing-step errors by introducing an explicit planning phase. PS+ prompting extends that by adding instructions to extract variables and verify intermediate calculations, targeting calculation errors as well.

The PS and PS+ trigger sentences

PS prompting replaces 'Let's think step by step' with a two-sentence trigger: 'Let's first understand the problem and devise a plan to solve the problem. Then, let's carry out the plan and solve the problem step by step.' The addition of a planning phase before execution asks the model to decompose the problem before attempting to solve any part of it. PS+ prompting extends this with more specific instructions. The full PS+ trigger reads: 'Let's first understand the problem, extract relevant variables and their corresponding numerals, and make a plan. Then, let's carry out the plan, calculate intermediate variables (pay attention to correct numerical calculation and commonsense), solve the problem step by step, and show the answer.' The instruction to extract variables explicitly forces the model to map problem text to symbolic quantities before computing. The reminder to pay attention to correct numerical calculation targets arithmetic mistakes. Both triggers are used in the same two-step pipeline as Zero-Shot-CoT: step one generates the reasoning chain, and step two extracts the final answer using a second prompt.

• PS trigger: 'Let's first understand the problem and devise a plan to solve the problem. Then, let's carry out the plan and solve the problem step by step.'
• PS+ trigger: adds variable extraction, intermediate calculation, and an explicit reminder to check numerical results before stating the answer.
• Both use a two-step pipeline: one call for the reasoning chain, one call for answer extraction (e.g., 'Therefore, the answer (arabic numerals) is').
• No demonstrations are required; the entire method is zero-shot.

Benchmark results across ten datasets

The paper evaluates PS and PS+ prompting on ten public datasets using GPT-3 (text-davinci-003). The dataset set covers six arithmetic reasoning benchmarks (AQuA, GSM8K, MultiArith, AddSub, SingleEq, SVAMP), two commonsense reasoning benchmarks (CommonsenseQA, StrategyQA), and two symbolic reasoning benchmarks (Last Letters and Coin Flip). On arithmetic tasks, Zero-Shot-CoT scores 56.4% on GSM8K and 69.9% on SVAMP. PS prompting improves those to 58.2% and 72.0%. PS+ reaches 59.3% on GSM8K and 75.7% on SVAMP. On symbolic reasoning, PS+ reaches 75.2% on Last Letters (compared to 65.2% for Zero-Shot-CoT and 70.6% for Manual-CoT) and 99.6% on Coin Flip (compared to 96.8% for Zero-Shot-CoT). The pattern holds across all ten datasets: PS+ consistently outperforms Zero-Shot-CoT, and on symbolic and some arithmetic tasks it exceeds the manually crafted demonstrations used in few-shot CoT. The paper also reports that PS+ prompting is comparable to or exceeds Zero-Shot Program-of-Thought Prompting, a competing zero-shot approach that generates executable Python code rather than natural-language reasoning.

Self-consistency amplifies the gains

Self-consistency, introduced by Wang et al. (2022), generates multiple reasoning paths for the same question and takes the majority vote across answers. It is model-agnostic and orthogonal to any specific trigger sentence. The Plan-and-Solve paper tests PS+ combined with self-consistency on GSM8K and SVAMP. PS+ with self-consistency reaches 73.7% on GSM8K and 84.4% on SVAMP, compared to 59.3% and 75.7% for PS+ without self-consistency. The combination outperforms self-consistency applied to Zero-Shot-CoT (56.4% and 69.9% without self-consistency as a baseline) by a substantial margin on both datasets. This means the two techniques are complementary: PS+ reduces per-path errors by structuring the reasoning, and self-consistency reduces variance by aggregating across paths. Users who are already applying self-consistency to Zero-Shot-CoT can improve results further by switching the trigger to PS+, with no other changes to the inference pipeline.

Practical use and adapting PS+ to new tasks

Plan-and-Solve prompting is zero-shot, which means the only change required is the trigger sentence. No demonstrations need to be collected or reviewed. The PS+ trigger was designed for arithmetic reasoning, where variable extraction and numerical checking are meaningful, but the authors evaluate it on commonsense and symbolic tasks as well and report consistent gains. For new tasks, the PS+ trigger can be adapted by replacing the domain-specific instruction ('extract relevant variables and their corresponding numerals') with a task-appropriate equivalent. For a legal reasoning task, that might be 'identify the relevant statutes and their conditions.' For a scientific question, it might be 'identify the quantities and their units.' The planning phase instruction generalizes broadly. The code for all experiments is available at github.com/AGI-Edgerunners/Plan-and-Solve-Prompting. PromptingIndex covers Plan-and-Solve prompting alongside Zero-Shot-CoT (Kojima et al. 2022), Auto-CoT (Zhang et al. 2022), self-consistency (Wang et al. 2022), and Least-to-Most Prompting (Zhou et al. 2022), all of which address different aspects of eliciting reliable multi-step reasoning from large language models without fine-tuning.

The core insight of Plan-and-Solve prompting is that the quality of zero-shot reasoning depends on what the trigger asks the model to do, not just on whether the model reasons at all. 'Let's think step by step' is permissive: it invites any reasoning path. 'Let's first understand the problem and devise a plan' is directive: it imposes a structure in which planning precedes execution. The empirical gains across ten diverse benchmarks suggest that this structural constraint is doing real work, reducing missing-step errors by forcing the model to enumerate subtasks upfront and reducing semantic misunderstanding by requiring the model to demonstrate comprehension in the planning phase before committing to a solution path.