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'''你是算法竞赛金牌选手。请逐步推导再给出最终答案，每一步标记并解释推理依据。\n问题：给定数组 nums = [3, 1, 4, 2, 5, 8, 7, 6]，求最长递增子序列的长度。\n思考步骤：\n步骤1：\n步骤2：\n步骤3：\n最终答案（仅数字）：'''\n\nclass ProductCategorizeResult(BaseModel):\n    reasoning: list[str] = Field(description=\"分类判断过程，每个维度一条\")\n    category: str = Field(description=\"必须属于 [Electronics, Fashion, Books, Home, Other]\")\n    confidence: float = Field(ge=0.0, le=1.0)\n    matched_keywords: list[str] = Field(default_factory=list)\n\nasync def few_shot_transform(raw: str) -> str:\n    r = await client.chat.completions.create(\n        model=\"gpt-4o-mini\", temperature=0.3,\n        messages=[{\"role\": \"user\", \"content\": FEW_SHOT_PROMPT.format(raw_input=raw)}])\n    return r.choices[0].message.content or \"\"\n\nasync def categorize_structured(title: str, desc: str) -> dict[str, Any]:\n    r = await client.chat.completions.create(\n        model=\"gpt-4o-mini-2024-07-18\", temperature=0.0,\n        messages=[{\"role\": \"user\", \"content\": f\"商品标题 {title}\\n描述 {desc}\"}],\n        response_format={\"type\": \"json_object\"})\n    data = json.loads(r.choices[0].message.content or \"{}\")\n    return ProductCategorizeResult(**data).model_dump()\n```\n```\n\n## CoT 思维链 & 结构化输出\n\n需要复杂推理（逻辑\u002F数学\u002F代码调试）时，显式要求模型分步骤推理，最后才给结论，准确率平均提升 15-30%。要喂给下游系统的结果，用 Pydantic + response_format 强制 JSON 模式，失败重试兜底，避免自由文本解析。\n\n| 技术 | 解决问题 | 最佳温度 | 典型应用场景 |\n|------|---------|---------|-------------|\n| Zero-Shot 纯指令 | 任务简单标准 | 0.1-0.3 | 翻译、摘要、格式转换 |\n| Few-Shot 示例注入 | 风格\u002F格式特殊要求 | 0.2-0.5 | 文案改写、标签标注、代码风格统一 |\n| CoT 思维链分步 | 多步推理\u002F数学\u002F逻辑 | 0.0-0.3 | 算法题、代码调试、根因分析 |\n| JSON Schema 结构化 | 对接程序接口 | 0.0 固定 | 打标入库、字段抽取、函数调用 |\n\n## 最佳实践\n\n写 Prompt 先给角色（System Prompt），再给上下文+任务，再给约束（字数\u002F格式\u002F语气\u002F禁忌）。迭代：用 20 条样本测真实准确率，失败案例回灌为 few-shot 示例，每次改进都有量化依据。","系统入门 Prompt Engineering 三大核心技术：Few-Shot 示例学习注入专业领域风格、Chain-of-Thought (CoT) 思维链引导复杂推理、JSON Schema 强制结构化输出对接下游系统。附真实 prompt 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