------
## 最终结论
```python
def largest_smallest_integers(lst):
    max_negative = None
    min_positive = None
    
    for num in lst:
        if num < 0:  # Check if the number is negative
            if max_negative is None or num > max_negative:
                max_negative = num
        elif num > 0:  # Check if the number is positive
            if min_positive is None or num < min_positive:
                min_positive = num
    
    return (max_negative, min_positive)
```