Your personal operating system for career transition.

Implement an in-memory PriorityInferenceQueue that:

1. Accepts inference requests with a priority field: "high", "normal", or "low"
2. Always dequeues high-priority requests before normal, and normal before low
3. Returns None from dequeue() if the queue is empty
4. Exposes a depth() method returning a dict with counts per priority level and a total key
5. Is safe for use with asyncio (use asyncio.Queue or equivalent, not threading primitives)

import asyncio
from dataclasses import dataclass

@dataclass
class InferenceRequest:
    request_id: str
    messages: list[dict]
    priority: str  # "high", "normal", "low"

class PriorityInferenceQueue:
    def __init__(self):
        # TODO: initialize separate queues per priority level
        pass

    async def enqueue(self, request: InferenceRequest) -> None:
        # TODO: add to the correct priority queue
        raise NotImplementedError

    async def dequeue(self) -> InferenceRequest | None:
        # TODO: return highest-priority item, or None if empty
        raise NotImplementedError

    def depth(self) -> dict:
        # TODO: return {"high": n, "normal": n, "low": n, "total": n}
        raise NotImplementedError