feat: implement new claude skills and workflow

.claude/skills/problem-analysis/README.md

@@ -0,0 +1,45 @@
+# Problem Analysis
+
+LLMs jump to solutions. You describe a problem, they propose an answer. For
+complex decisions with multiple viable paths, that first answer often reflects
+the LLM's biases rather than the best fit for your constraints. This skill
+forces structured reasoning before you commit.
+
+The skill runs through six phases:
+
+| Phase       | Actions                                                                  |
+| ----------- | ------------------------------------------------------------------------ |
+| Decompose   | State problem; identify hard/soft constraints, variables, assumptions    |
+| Generate    | Create 2-4 distinct approaches (fundamentally different, not variations) |
+| Critique    | Specific weaknesses; eliminate or refine                                 |
+| Verify      | Answer questions WITHOUT looking at solutions                            |
+| Cross-check | Reconcile verified facts with original claims; update viability          |
+| Synthesize  | Trade-off matrix with verified facts; decision framework                 |
+
+## When to Use
+
+Use this for decisions where the cost of choosing wrong is high:
+
+- Multiple viable technical approaches (Redis vs Postgres, REST vs GraphQL)
+- Architectural decisions with long-term consequences
+- Problems where you suspect your first instinct might be wrong
+
+## Example Usage
+
+```
+I need to decide how to handle distributed locking in our microservices.
+Options I'm considering:
+
+- Redis with Redlock algorithm
+- ZooKeeper
+- Database advisory locks
+
+Use your problem-analysis skill to structure this decision.
+```
+
+## The Design
+
+The structure prevents premature convergence. Critique catches obvious flaws
+before costly verification. Factored verification prevents confirmation bias --
+you answer questions without seeing your original solutions. Cross-check forces
+explicit reconciliation of evidence with claims.