Describe the bug

When using LiteLLM with models that return reasoning_content (e.g., Gemini 2.5 with thinking enabled), the reasoning/thought content is correctly captured and stored as types.Part objects with thought=True in ADK v1.20.0. However, when building subsequent LLM requests, the _get_content() function does not filter out these thought parts, causing:

1. Reasoning content to be sent back to the LLM as regular content in subsequent turns
2. Significant token waste from replaying thought traces
3. Potential model confusion from seeing its own reasoning as conversation content

To Reproduce

1. Install ADK v1.20.0: pip install google-adk==1.20.0
2. Create an agent using LiteLLM adapter with a reasoning model:

from google.adk.agents import Agent
from google.adk.models.lite_llm import LiteLlm

agent = Agent(
    name="test_agent",
    model=LiteLlm(model="gemini/gemini-2.5-pro"),  # or other model with reasoning_content
    instruction="You are a helpful assistant."
)

3. Run a multi-turn conversation (2+ messages)
4. Observe in LiteLLM logs that turn 2+ includes the reasoning text from turn 1 as regular message content

Error/Log output:

Turn 2 request to LLM contains reasoning text from turn 1 as regular content field instead of being filtered out.

Expected behavior

Thought parts (with thought=True) should be filtered from the conversation history when building LLM requests, similar to how _convert_foreign_event() in contents.py already filters them (line 513).

Screenshots

N/A - Visible in LiteLLM proxy logs or by adding debug logging to _get_content().

Desktop (please complete the following information):

• OS: macOS
• Python version: 3.11
• ADK version: 1.20.0+

Model Information:

• Are you using LiteLLM: Yes
• Which model is being used: gemini-2.5-pro (any model returning reasoning_content)

Additional context

Root Cause Analysis:

Commit 31cfa3b82bff2a130622d3ba0909024927121ce4 ("feat: Capture thinking output, forward raw payloads, and fix exec locals") added _convert_reasoning_value_to_parts() to capture reasoning as thought parts, but _get_content() (line 536 in lite_llm.py) was not updated to filter them:

# Current code (buggy)
async def _get_content(parts: Iterable[types.Part], ...):
  for part in parts:
    if part.text:  # Missing: and not part.thought
      content_objects.append({"type": "text", "text": part.text})

Suggested Fix:

async def _get_content(parts: Iterable[types.Part], ...):
  for part in parts:
    if part.thought:
      continue  # Skip thought/reasoning parts
    if part.text:
      content_objects.append({"type": "text", "text": part.text})

Related:

• Commit that introduced the bug: 31cfa3b82bff2a130622d3ba0909024927121ce4
• Similar filtering pattern exists in contents.py:_convert_foreign_event() (line 513): if part.thought: continue
• This was working correctly in ADK v1.19.0 (before reasoning capture was added)