refactor(mode-prompts): migrate analyze prompt

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/hooks/keyword-detector/analyze/default.ts

@@ -1,3 +1,5 @@
+import { ANALYZE_MODE_PROMPT } from "@oh-my-opencode/prompts-core"
+
 /**
  * Analyze mode keyword detector.
  *
@@ -12,19 +14,4 @@
 export const ANALYZE_PATTERN =
   /\b(analyze|analyse|investigate|examine|research|study|deep[\s-]?dive|inspect|audit|evaluate|assess|review|diagnose|scrutinize|dissect|debug|comprehend|interpret|breakdown|understand)\b|why\s+is|how\s+does|how\s+to|분석|조사|파악|연구|검토|진단|이해|설명|원인|이유|뜯어봐|따져봐|평가|해석|디버깅|디버그|어떻게|왜|살펴|分析|調査|解析|検討|研究|診断|理解|説明|検証|精査|究明|デバッグ|なぜ|どう|仕組み|调查|检查|剖析|深入|诊断|解释|调试|为什么|原理|搞清楚|弄明白|phân tích|điều tra|nghiên cứu|kiểm tra|xem xét|chẩn đoán|giải thích|tìm hiểu|gỡ lỗi|tại sao/i
 
-export const ANALYZE_MESSAGE = `[analyze-mode]
-ANALYSIS MODE. Gather context before diving deep:
-
-CONTEXT GATHERING (parallel):
-- 1-2 explore agents (codebase patterns, implementations)
-- 1-2 librarian agents (if external library involved)
-- Direct tools: Grep, AST-grep, LSP for targeted searches
-
-IF COMPLEX - DO NOT STRUGGLE ALONE. Consult specialists:
-- **Oracle**: Conventional problems (architecture, debugging, complex logic)
-- **Artistry**: Non-conventional problems (different approach needed)
-
-SYNTHESIZE findings before proceeding.
----
-MANDATORY delegate_task params: ALWAYS include load_skills and run_in_background when calling delegate_task. Evaluate available skills before dispatch - pass task-appropriate skills when relevant, pass [] ONLY when no skill matches the task domain.
-Example: delegate_task(subagent_type="explore", prompt="...", run_in_background=true, load_skills=[])`
+export const ANALYZE_MESSAGE = ANALYZE_MODE_PROMPT