fix: resolve infinite loop when combining outputSchema and tools also added unit tests

[b2rpt]

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docs/contributing-guide/) before creating a pull request.

### Link to Issue or Description of Change

**1. Link to an existing issue (if applicable):**

- Closes: #411
- Related: https://github.com/google/adk-js/issues/411

**2. Or, if no issue exists, describe the change:**

**Problem:**
When an agent is configured with both `outputSchema` and tools:
1. The `BasicLlmRequestProcessor` sets `responseMimeType: "application/json"` and

responseSchema on the model configuration.
2. In the Gemini API, combining strict JSON mode and Function Calling (tools) in the same
call is architecturally unsupported:
- Stable models immediately return a 400 Bad Request API error.
- Preview models (such as gemini-3.1-flash-lite) get confused, calling tools
recursively and getting trapped in an infinite loop.

**Solution:**
We implemented the **Tool-Based Structured Output** pattern (aligning with `adk-python`):
1. **API-level bypass**: If tools are present, we bypass setting `responseMimeType:

"application/json"andresponseSchema at the Gemini API level (BasicLlmRequestProcessor), allowing standard function calling without API conflicts. 2. **Dynamic Tool Registration**: In LlmAgent.ts, we dynamically inject a special set_model_responsetool into the agent's toolset whenoutputSchemaand tools are both present. 3. **Filter Bypass**: Ensured that theset_model_responsetool is never filtered out by plugin-drivenallowedToolsrestrictions. 4. **System Instruction Injection**: Appended a system instruction instructing the model that it must submit its final structured output by calling theset_model_responsetool. 5. **Turn Interception**: Intercepted theset_model_responsecall in the agent's post- processing lifecycle to parse the arguments and format the final text JSON response, settingskipSummarization = true to break the agent execution loop and exit the turn immediately. Added safe-checks for TS compiler compatibility (toolContext` null-checks).

---

### Testing Plan

**Unit Tests:**

- [x] I have added or updated unit tests for my change.
- [x] All unit tests pass locally.

**Summary of unit test results:**
Run successfully via Vitest (`vitest --project unit:core --project unit:dev --run`):
- `basic_llm_request_processor_test.ts`: Passed (9 tests, including new verification that

outputSchema is not set at API level when tools are present).
- instructions_llm_request_processor_test.ts: Passed (5 tests, including new
verification that instructions to call set_model_response are successfully appended).
- Total test suite: 1,787 test cases successfully executed and passed.

**Manual End-to-End (E2E) Tests:**
To manually verify, run an agent configured with an `outputSchema` and one or more custom

tools. The agent will successfully execute the custom tools and then return a single
structured JSON response by calling set_model_response at the end of the turn without
triggering a 400 Bad Request or entering recursive tool call loops.

---

### Checklist

- [x] I have read the [CONTRIBUTING.md](https://github.com/google/adk-

js/blob/main/CONTRIBUTING.md) document.
- [x] I have performed a self-review of my own code.
- [x] I have commented my code, particularly in hard-to-understand areas.
- [x] I have added tests that prove my fix is effective or that my feature works.
- [x] New and existing unit tests pass locally with my changes.
- [x] I have manually tested my changes end-to-end.
- [ ] Any dependent changes have been merged and published in downstream modules.

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