Loop agent overwrites state's output key when invoking exit_loop tool

**Describe the bug**

This is a bug in the [LoopAgents demo](https://google.github.io/adk-docs/agents/workflow-agents/loop-agents/). The demo shows an iterative writing pipeline.

1. An initial writer agent produces an output and assigns it to a state key CURRENT_DOC.
2. LoopAgent
a. A LLMAgent writes feedback and outputs it to another state key. If no feedback, it outputs COMPLETION_PHRASE
b. A LLMAgent uses that feedback to re-write the document, outputting it to the same state key CURRENT_DOC. If COMPLETION_PHRASE is present in feedback, it doesnt output anything and calls `exit_loop` tool.

**To Reproduce**

Steps to reproduce the behavior:
1. Copy/run [LoopAgents demo](https://google.github.io/adk-docs/agents/workflow-agents/loop-agents/) in adk ui (`adk web --log_level DEBUG --port 8000 path/to/agent/dir`
2. Run the agent with some topic.
3. Observe that there is no final output. Observe that `state[current_document]` is now an empty string when the invocation ends.

**Expected behavior**

The last unmodified state value is propagated through the end of the loop. This seems to be the intent of the demo, but it doesn't work.

**Screenshots**

The state variable during intermediate events in the agent invocation:

The final state is empty:

**Versions**

- OS: Linux
- ADK version: 1.25.1
- Python version: 3.11