[Feature]: Refactor the logic in tool parser manager and reasoning parser manager

[gaocegege]

🚀 The feature, motivation and pitch

#14428 (comment) / #14428 (comment)

The implementation of the tool parser manager and reasoning parser manager could be optimized.

/cc @aarnphm

Alternatives

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Additional context

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[aarnphm]

oh update for @gaocegege I'm working on a separate library for parser, will release soon, so will be a part of this meta issue.

[gaocegege]

@aarnphm It's awesome. Looking forward to it!