[v0][structured output] Support reasoning output

[gaocegege]

Ref #12619

Only apply Guided/Structured grammar after reasoning steps in Reasoning models. It enabled reasoning outputs for xgrammar and outlines, didn't support lm-format-enforcer.

Usage:

vllm serve deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B --enable-reasoning --reasoning-parser deepseek_r1

prompt = ("Generate a JSON with the brand, model and car_type of"
          "the most iconic car from the 90's, think in 100 tokens")
completion = client.chat.completions.create(
    model="deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B",
    messages=[{
        "role": "user",
        "content": prompt,
    }],
    extra_body={"guided_json": json_schema},
)
print("content: ", completion.choices[0].message.content)
print("reasoning_content: ", completion.choices[0].message.reasoning_content)

content: {

"brand": "Levels",
"model": "racing equation",
"car_type": "sedan"
}
reasoning_content:  
Okay, the user is asking me to generate a JSON with the brand, model, and car type of the most iconic 90s car. I need to make sure it's within 100 tokens. Let me start by recalling some of the most significant cars from the 90s.型号 race cars are a big category, so theathy and V8 are definitely in there.马路超车 automotive should be in as well.

I need to find the brand.Levels was really influential, especially in racing. So the brand should be Levels. The model is the race car itself, maybe racing equations since they were a big trend. The engine details: a 7.5-litreUnused to make sense of the information, but I'll have to include it as it's important for the context.

Fact checking is crucial. The 90s included the Formula 1 series, which was growing. Yes, L charcoal was a key driver there. Values of engines and tests set a benchmark. B gjvertern is part of the马路 coder project, and P race appears to be another race series.

I should structure the JSON without parentheticals and make sure each field is clearly defined. Let me make a mental note to keep it concise. I'll write the JSON, making sure it neither uses more than 90 tokens nor exceeds that number. Finally, I'll double-check to ensure accuracy without making any mistakes.

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[gaocegege]

@russellb Could you please help review this PR?

[gaocegege]

Please let me know if anyone is ready to review and merge this. Once confirmed, I will resolve the conflicts here. It’s time-consuming to address them daily.

[aarnphm]

I have few questions regarding implementations, otherwise lgtm

[mergify]

This pull request has merge conflicts that must be resolved before it can be
merged. Please rebase the PR, @gaocegege.

https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/working-with-forks/syncing-a-fork

[mgoin]

Thanks for the great progress on this feature @gaocegege !

[gaocegege]

Thanks for your review @aarnphm @mgoin