Add LiteLLM setup documentation

Created comprehensive guide for configuring LLMX with LiteLLM:
- Environment variable setup
- Configuration file format
- Correct usage patterns (separate provider and model)
- Common error troubleshooting
- Model name format documentation

Key points:
- Use `-c model_provider=litellm` NOT `litellm:` prefix
- Set LITELLM_BASE_URL and LITELLM_API_KEY
- LiteLLM provider uses Chat Completions API (wire_api=chat)

🤖 Generated with Claude Code

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

LITELLM-SETUP.md

@@ -0,0 +1,76 @@
+# LLMX with LiteLLM Configuration Guide
+
+## Quick Start
+
+### 1. Set Environment Variables
+
+```bash
+export LITELLM_BASE_URL="https://llm.ai.pivoine.art/v1"
+export LITELLM_API_KEY="your-litellm-master-key"
+```
+
+### 2. Create Configuration File
+
+Create `~/.llmx/config.toml`:
+
+```toml
+model_provider = "litellm"
+model = "anthropic/claude-sonnet-4-20250514"
+```
+
+### 3. Run LLMX
+
+```bash
+# Use default config
+llmx "hello world"
+
+# Override model
+llmx -m "openai/gpt-4" "hello world"
+
+# Override provider and model
+llmx -c model_provider=litellm -m "anthropic/claude-sonnet-4-20250514" "hello"
+```
+
+## Important Notes
+
+### DO NOT use provider prefix in model name
+❌ Wrong: `llmx -m "litellm:anthropic/claude-sonnet-4-20250514"`
+✅ Correct: `llmx -c model_provider=litellm -m "anthropic/claude-sonnet-4-20250514"`
+
+LLMX uses separate provider and model parameters, not a combined `provider:model` syntax.
+
+### Provider Selection
+
+The provider determines which API endpoint and format to use:
+- `litellm` → Uses Chat Completions API (`/v1/chat/completions`)
+- `openai` → Uses Responses API (`/v1/responses`) - NOT compatible with LiteLLM
+
+### Model Names
+
+LiteLLM uses `provider/model` format:
+- `anthropic/claude-sonnet-4-20250514`
+- `openai/gpt-4`
+- `openai/gpt-4o`
+
+Check your LiteLLM configuration for available models.
+
+## Troubleshooting
+
+### Error: "prompt_cache_key: Extra inputs are not permitted"
+**Cause**: Using wrong provider (defaults to OpenAI which uses Responses API)
+**Fix**: Add `-c model_provider=litellm` or set `model_provider = "litellm"` in config
+
+### Error: "Invalid model name passed in model=litellm:..."
+**Cause**: Including provider prefix in model name
+**Fix**: Remove the `litellm:` prefix, use just the model name
+
+### Error: "Model provider `litellm` not found"
+**Cause**: Using old binary without LiteLLM provider
+**Fix**: Use the newly built binary at `llmx-rs/target/release/llmx`
+
+## Binary Location
+
+Latest binary with LiteLLM support:
+```
+/home/valknar/Projects/codex/llmx/llmx-rs/target/release/llmx
+```