\section{Prompt Templates and Few-Shot Library}
\label{sec:appendix-prompts}
\label{appendix:prompts}

This appendix provides the full prompt templates, label definitions, confusion guides, and few-shot libraries used in each stage of \framework{}. All components are dynamically assembled during inference based on the current branch (Step~1/2/3) and the Gate's output.

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\subsection{Step 1: Confidence-Aware Gate Prompt}
\label{sec:appendix-gate}

The Step~1 Gate prompt is responsible for the preliminary 4-class decision (3 Non-Reply + OTHER) and outputting confidence (High/Medium/Low).
Key design points include: (1) defining necessary and sufficient conditions for each Non-Reply class (e.g., \emph{Declining to answer} requires an explicit refusal or deferral); (2) operationalizing confidence levels---High is permitted only when the answer is short, unambiguous, and contains no substantive information; (3) requiring Chain-of-Thought analysis before label output to reduce premature judgments based on surface cues.
\lstinputlisting{appendix_assets/step1/task2_5.2_gate_v3_confidence.txt}

\subsection{Base Dynamic Prompt Template (Step 2/3)}
\label{sec:appendix-dynamic-template}
Step~2 and Step~3 share a base dynamic template structured as: System Instructions $\rightarrow$ Label Definitions $\rightarrow$ Confusion Guide $\rightarrow$ Few-shot Examples (Anchors + Boundaries) $\rightarrow$ Input Sample $\rightarrow$ CoT Reasoning Format Requirement.
During assembly, the Prompt Builder performs the following substitutions based on branch type: (1) Label Space---Step~2 uses full 9-class definitions, Step~3 uses 6-class definitions (excluding the three Non-Reply classes); (2) Confusion Guide---Step~2 dynamically selects discrimination points relevant to the Gate label, Step~3 uses a generic confusion guide for the Ambivalent branch; (3) Few-shot Quantity---Step~2 sets $B{=}3$ boundaries, Step~3 sets $B{=}10$ boundaries to cover more confusion pairs.
\lstinputlisting{appendix_assets/template/stage2_dynamic_template.txt}

\subsection{Label Definitions (9-class / 6-class)}
\label{sec:appendix-definitions}

Label definitions are the core component of the prompt. We significantly expanded upon the concise definitions in the original paper~\citep{thomas2024ineversaidthat} to form a set of refined, operational label definitions.
Principles for expansion include: (1) Providing necessary and sufficient conditions rather than just descriptive text, e.g., the definition of \emph{Implicit} explicitly requires "the answer provides information from which a response to the sub-question can be reasonably inferred, but does not state it directly using the same terms or structure as the question"; (2) Appending "Distinction from Similar Classes" notes at the end of each definition, e.g., emphasizing in the \emph{General} definition that "if the answer contains specific inferable information, it should be classified as Implicit even if phrased generally"; (3) Providing more specific criteria for minority classes (e.g., \emph{Partial/half-answer}) to reduce misclassification.
\vspace{1em}
The full 9-class refined definitions used in Step~2 are listed below. The 6-class definitions (Step~3) follow the same structure with the three Non-Reply classes removed; the complete version is available in our code repository.
\lstinputlisting{appendix_assets/definitions/defs_9class_v1.txt}

\subsection{Confusion Guides}
\label{sec:appendix-confusion-guides}

Confusion guides provide structured discrimination rules targeting high-frequency misclassification pairs found in training set zero-shot reasoning.
Each guide typically contains 3--5 rules, describing a condition "If ..., then classify as X instead of Y".
For example, the confusion guide for \emph{Declining to answer} targets common misclassifications such as \emph{Declining}$\rightarrow$\emph{Dodging}, emphasizing "If the answer provides any content related to the sub-question topic (even indirectly), do not classify as Declining".
Confusion guides are dynamically selected in Step~2 based on the Gate label to ensure only relevant discrimination rules are injected, avoiding excessive context length.
As a representative example, the confusion guide for \emph{Declining to answer} is shown below. The remaining confusion guides (\emph{Claims ignorance}, \emph{Clarification}, and the \emph{Ambivalent} branch) follow the same structure and are available in our code repository.
\lstinputlisting{appendix_assets/confusion_guides/confusion_guide_declining.txt}

\subsection{Few-Shot Library Used by the Prompt Builder}
\label{sec:appendix-fewshots}

The few-shot library is divided into two categories: \textbf{Anchors} (Positive Examples) and \textbf{Boundaries} (Hard Negative Counter-Examples).

We mine \textbf{anchors} by selecting representative training samples that DeepSeek-V3 classifies correctly in a zero-shot setting. Selection prioritizes: (1) high confidence; (2) moderate length (avoiding too short or too long); (3) clear embodiment of core class features.

We mine \textbf{boundaries} from the confusion matrix of training set zero-shot reasoning. For each high-frequency misclassification pair (e.g., \emph{Dodging}$\rightarrow$\emph{Declining}), we select misclassified samples along with their correct labels to form "Predicted Label vs. True Label" contrastive examples.
During inference, the Prompt Builder annotates "Predicted: X, but correct label is Y" before each boundary example to provide an explicit correction signal.
This "teaching by error" strategy ensures few-shot budget is precisely invested in decision boundaries prone to mistakes, rather than evenly distributed across all classes.

At runtime, the Prompt Builder selects from the library based on priority according to the current step configuration ($K$ anchors, $B$ boundaries). Step~2 uses $K{=}2, B{=}3$ (focusing on Non-Reply correction), Step~3 uses $K{=}6, B{=}10$ (broad coverage of confusion pairs among 6 classes). As a representative example, the anchor and boundary pools for \emph{Declining to answer} are listed below. The complete libraries for all classes are available in our code repository.

\vspace{1em}
\lstinputlisting{appendix_assets/fewshots/declining/anchors.jsonl}
\lstinputlisting{appendix_assets/fewshots/declining/boundaries.jsonl}
