Update AI workflow with exact user request and correct model info

Author: arnavk23

AI_WORKFLOW.md

@@ -1,9 +1,104 @@
 # AI-Assisted Problem Generation Workflow
 
+## Motivation
+After successful generation, the user asked (verbatim):
+> "Ok. In that case, could you please explain your workflow and the steps you took? What model? What prompt(s)? What input? Etc."
+>
+> "In the end, we want something reproducible and that we can script with one of the models' API. Also, each model needs documentation."
+
+This document addresses that requirement: full reproducibility for API scripting.
+
 ## Model & Tools Used
-- **Model:** Claude Haiku 3.5 (via GitHub Copilot)
-- **IDE:** VS Code with Copilot Chat
-- **Code tools:** grep_search, file_search, read_file, replace_string_in_file, multi_replace_string_in_file, get_errors
+- **Model used in this run:** GPT-5.3-Codex (via GitHub Copilot Chat in VS Code)
+- **IDE:** VS Code with GitHub Copilot Chat extension
+- **Code tools:** grep_search, file_search, read_file, replace_string_in_file, multi_replace_string_in_file, get_errors, fetch_webpage
+
+## Scripting with Model APIs
+
+### Claude (Anthropic API)
+**Model:** `claude-3-5-haiku-20241022` (recommended for code tasks)
+
+**Installation:**
+```bash
+pip install anthropic
+```
+
+**Environment:**
+```bash
+export ANTHROPIC_API_KEY="sk-ant-..."
+```
+
+**Basic usage:**
+```python
+import anthropic
+
+client = anthropic.Anthropic()
+
+message = client.messages.create(
+    model="claude-3-5-haiku-20241022",
+    max_tokens=4096,
+    messages=[
+        {"role": "user", "content": "Your prompt here"}
+    ]
+)
+
+print(message.content[0].text)
+```
+
+### OpenAI GPT API
+**Model:** `gpt-4-turbo` or `gpt-3.5-turbo`
+
+**Installation:**
+```bash
+pip install openai
+```
+
+**Environment:**
+```bash
+export OPENAI_API_KEY="sk-..."
+```
+
+**Basic usage:**
+```python
+from openai import OpenAI
+
+client = OpenAI()
+
+response = client.chat.completions.create(
+    model="gpt-4-turbo",
+    messages=[
+        {"role": "user", "content": "Your prompt here"}
+    ]
+)
+
+print(response.choices[0].message.content)
+```
+
+### Google Gemini API
+**Model:** `gemini-2.0-flash`
+
+**Installation:**
+```bash
+pip install google-generativeai
+```
+
+**Environment:**
+```bash
+export GOOGLE_API_KEY="AIzaSy..."
+```
+
+**Basic usage:**
+```python
+import google.generativeai as genai
+
+genai.configure(api_key=os.environ.get("GOOGLE_API_KEY"))
+model = genai.GenerativeModel("gemini-2.0-flash")
+
+response = model.generate_content("Your prompt here")
+print(response.text)
+```
+
+---
 
 ## User Prompts (2 iterations)