## Bug Report

**LiteLLM version:** 1.81.16 (also reproduced conceptually on 1.80.10+)

### Description

Multi-turn tool calling through the **Responses API** (`/v1/responses`) fails
when routing to **Vertex AI Anthropic (Claude)** models. The same requests
succeed via Chat Completions (`/v1/chat/completions`) to the same models.

Single-turn tool calls work. The failure occurs on the **2nd+ tool call turn**
in a multi-turn conversation.

### Error

```
litellm.BadRequestError: Vertex_aiException BadRequestError -
  "tool_use ids were found without tool_result blocks immediately after:
   toolu_vrtx_01MWvTJiSMaC4cndrp3sB8WX. Each tool_use block must have
   a corresponding tool_result block in the next message."
```

### Root Cause (hypothesis)

The Responses API path performs a double translation:
1. Responses API input → internal Chat Completions format
2. Internal Chat Completions → Anthropic Messages API format

During this double hop, the `tool_use` / `tool_result` block pairing gets
corrupted on multi-turn conversations. Vertex AI (Anthropic) then rejects
the malformed message because tool_use blocks lack corresponding tool_result
blocks in the immediately following message.

### Reproduction

**Fails (Responses API → Claude):**
```python
from openai import OpenAI

client = OpenAI(base_url="http://localhost:4000", api_key="sk-...")

# Turn 1: user asks something requiring tools
response = client.responses.create(
    model="claude-sonnet-4-5",
    input=[{"role": "user", "content": "What's the weather in SF and NYC?"}],
    tools=[{
        "type": "function",
        "function": {
            "name": "get_weather",
            "description": "Get weather for a city",
            "parameters": {
                "type": "object",
                "properties": {"city": {"type": "string"}},
                "required": ["city"]
            }
        }
    }]
)
# Turn 1 succeeds — model makes tool_calls

# Turn 2: send tool results back and continue
# THIS is where it breaks — the tool_use/tool_result message ordering
# is corrupted during Responses → Chat Completions → Anthropic translation
```

**Works (Chat Completions → same Claude model):**
```python
response = client.chat.completions.create(
    model="claude-sonnet-4-5",
    messages=[...],  # same conversation
    tools=[...]      # same tools
)
# Multi-turn works perfectly via Chat Completions
```

**Works (Responses API → GPT models):**
```python
response = client.responses.create(
    model="gpt-4.1",  # Azure path — no Anthropic translation
    input=[...],
    tools=[...]
)
# Multi-turn works via Responses API to non-Anthropic backends
```

### Test Matrix

| Scenario | API | Backend | Result |
|----------|-----|---------|--------|
| Multi-turn tool calls | Chat Completions | Claude (Vertex AI) | ✅ PASS |
| Multi-turn tool calls | Responses | Claude (Vertex AI) | ❌ FAIL |
| Multi-turn tool calls | Responses | GPT (Azure) | ✅ PASS |
| Single tool call | Responses | Claude (Vertex AI) | ✅ PASS |

### Impact

This blocks any application that:
1. Uses the Responses API (e.g., Codex CLI, which now **requires** `wire_api = "responses"` and has removed Chat Completions support)
2. Routes to Claude/Anthropic models through LiteLLM
3. Uses multi-turn tool calling

This effectively makes **Claude models unusable through Codex CLI + LiteLLM**.

### Related Issues

- #6836 — Meta-issue for Anthropic tool calling problems
- #11804 — Anthropic duplicate tool_result handling
- #12020 — Tool input_schema type enforcement

### Environment

- LiteLLM: 1.81.16
- Provider: `vertex_ai` (Anthropic partner models)
- Models tested: claude-sonnet-4-5, claude-opus-4-5, claude-haiku-4-5
- Client: OpenAI Python SDK v1.x (Responses API)

### Suggested Investigation

The bug likely lives in the Responses API → internal message translation
layer, specifically how `tool_use` and `tool_result` blocks are ordered
when converting from Responses format to Chat Completions format before
the final Anthropic translation hop. The Anthropic Chat Completions path
(which skips the Responses → internal step) handles the same conversations
correctly.