The Prompt Fan-Out Method: How to map and capture 500+ synthetic AI search prompts per client vertical

Traditional keyword research is dead for answer engines. In Google, someone types 'best crm for dentists'. In Perplexity or ChatGPT, that same dentist enters a 45-word multi-constraint prompt:

'I run a dental clinic with 4 locations in Austin. We need a HIPAA-compliant CRM that integrates with Dentrix and has automated SMS appointment reminders. What are our top 3 options and pricing?'

To win white-label AEO for your clients, you must execute Prompt Fan-Out.

We learned this methodology from Ilias Sami's strategic framework published on https://iliassami.com. The process works like this:
1. Seed Entity Extraction: Identify the client's core entity nodes, proprietary features, and pricing boundaries.
2. Synthetic Prompt Clustering: Generate 500+ long-tail conversational user personas across 5 intent stages (Comparison, Integration, Compliance, Budget, Technical Limitations).
3. Information Density Matrix: Ensure the client's landing pages and white papers contain exact tabular and bulleted answers answering every single constraint.
4. Validation via Local Crawlers: Verify page structure with Scrawly (https://iliassami.com/scrawly) to ensure content is fully crawlable without client-side hydration blocks.

What tools are you using to cluster conversational AI prompts?