feat: Apply implementation-approach.md references to English version subagents

## Changes (English agents)
- technical-designer: Add implementation-approach.md to initial tasks, clarify Phase 1-4 execution
- work-planner: Add to initial tasks, specify L1/L2/L3 verification level usage
- task-executor: Improve progress update with concrete Edit tool instructions

## Improvements
- Ensures proper consideration of vertical/horizontal slicing strategies
- Prevents progress tracking omissions
- Improves AI execution accuracy across language environments

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: shinpr

.claude/agents-en/task-executor.md

@@ -66,7 +66,10 @@ ls docs/plans/tasks/*.md | grep -E "task-[0-9]{2}\.md$" | head -1
 ### 3. Implementation Execution
 - If all checkboxes are `[x]`, report "already completed" and end
 - Staged implementation with incremental verification
-- 3-location synchronized update upon each step completion
+- Upon each step completion【Required】Update checkboxes using Edit tool:
+  1. Task file: `[ ]` → `[x]`
+  2. Corresponding section in work plan: `[ ]` → `[x]`
+  3. Progress section in overall design document (if exists)
 - Run only added tests and confirm they pass (overall tests not needed)
 
 ### 3.5 Operation Verification【Mandatory】
@@ -97,6 +100,11 @@ Report in the following JSON format upon task completion (**without executing qu
   "filesModified": ["file1.ts", "file2.ts"],
   "testsAdded": ["test1.test.ts"],
   "newTestsPassed": true,
+  "progressUpdated": {
+    "taskFile": "5/8 items completed",
+    "workPlan": "Updated",
+    "designDoc": "N/A"
+  },
   "runnableCheck": {
     "level": "L1/L2/L3",
     "executed": true,
@@ -111,7 +119,7 @@ Report in the following JSON format upon task completion (**without executing qu
 
 ## Execution Principles
 
-- **3-location synchronized update**: Always update upon each action completion
+- **Progress checkbox update**: Always update `[ ]`→`[x]` using Edit tool upon each action completion
 - **Overall design document confirmation**: Required before implementation
 - **Complete self-containment**: Execute to the end without asking questions
 - **Test-first**: Adhere to Red-Green-Refactor process (follow project test rules)

.claude/agents-en/technical-designer.md

@@ -14,6 +14,7 @@ Before starting work, be sure to read and follow these rule files:
 - @docs/rules/typescript.md - TypeScript development rules
 - @docs/rules/ai-development-guide.md - AI development guide
 - @docs/rules/project-context.md - Project context
+- @docs/rules/architecture/implementation-approach.md - Metacognitive strategy selection process (used for implementation approach decisions)
 - @docs/rules/architecture/ architecture rule files (if exist)
   - Read if project-specific architecture rules are defined
   - Apply rules according to adopted architecture patterns
@@ -80,14 +81,15 @@ Must be performed at the beginning of Design Doc creation:
 Must be performed when creating Design Doc:
 
 1. **Approach Selection Criteria**
+   - Execute Phase 1-4 of @docs/rules/architecture/implementation-approach.md to select strategy
    - **Vertical Slice**: Complete by feature unit, minimal external dependencies, early value delivery
    - **Horizontal Slice**: Implementation by layer, important common foundation, technical consistency priority
    - **Hybrid**: Composite, handles complex requirements
-   - Document selection reason (consider feature complexity, dependencies, integration points)
+   - Document selection reason (record results of metacognitive strategy selection process)
 
 2. **Integration Point Definition**
    - Which task first makes the whole system operational
-   - Verification level for each task (defined in @docs/rules/architecture/implementation-approach.md)
+   - Verification level for each task (L1/L2/L3 defined in @docs/rules/architecture/implementation-approach.md)
 
 ### Change Impact Map【Required】
 Must be included when creating Design Doc.

.claude/agents-en/work-planner.md

@@ -15,6 +15,10 @@ Before starting work, be sure to read and follow these rule files:
 - @docs/rules/typescript-testing.md - Testing rules
 - @docs/rules/project-context.md - Project context
 - @docs/rules/typescript.md - TypeScript development rules
+- @docs/rules/architecture/implementation-approach.md - Implementation strategy patterns and verification level definitions (used for task decomposition)
+- @docs/rules/architecture/ architecture rule files (if exist)
+  - Read if project-specific architecture rules are defined
+  - Apply rules according to adopted architecture patterns
 
 ## Main Responsibilities
 
@@ -80,7 +84,7 @@ Include completion conditions in task names (e.g., "Service implementation and u
 ## Task Decomposition Principles
 
 ### Implementation Approach Application
-Determine task sequence based on the implementation approach (vertical/horizontal/hybrid slice) decided in the Design Doc.
+Decompose tasks based on the implementation approach decided in the Design Doc, following the integration point definitions and L1/L2/L3 verification levels from @docs/rules/architecture/implementation-approach.md.
 
 ### Task Dependency Minimization Rules
 - Dependencies up to 2 levels maximum (A→B→C acceptable, A→B→C→D requires redesign)