fix: extract reasoning_content from summary for DeepSeek compatibility

[yurekami]

Summary

• Fixes issue LiteLLM DeepSeek thinking mode fails with missing reasoning_conten on tool calls #2155 where LiteLLM with DeepSeek in thinking mode fails with multi-turn conversations that include tool calls
• Extracts reasoning_content from the summary field of reasoning messages
• Includes the extracted reasoning_content in assistant messages that have tool calls

Problem

When using the OpenAI Agents SDK with LiteLLM configured for DeepSeek's thinking mode (deepseek/deepseek-reasoner), multi-turn conversations with tool calls fail because:

1. DeepSeek API returns reasoning_content in the reasoning item's summary field
2. When the conversation history is sent back for subsequent turns, the reasoning_content field is missing from assistant messages
3. DeepSeek API requires this field in assistant messages for proper conversation continuity

Solution

The fix tracks pending_reasoning_content across message conversion:

1. When a reasoning message is encountered, extract the reasoning text from the summary field (which contains summary_text items)
2. Store it as pending_reasoning_content
3. When an assistant message with tool calls is flushed, include the pending reasoning_content

Test plan

• Added test for extracting reasoning_content from summary and including in assistant message with tool calls
• Added test for reasoning message without summary field (should not cause errors)
• Added test to verify reasoning_content is only added to the immediately following assistant message

🤖 Generated with Claude Code

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[chatgpt-codex-connector]

Concatenate all summary_text parts before setting reasoning_content

The reasoning summary is a list of parts, but the loop breaks on the first summary_text. If a reasoning item contains multiple summary_text entries (e.g., summaries emitted in multiple parts), only the first chunk is copied into reasoning_content, so the assistant message history will carry a truncated reasoning payload. This can still break DeepSeek continuity because the required reasoning content is incomplete. Consider concatenating all summary_text parts in order instead of stopping at the first one.

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