def nums_compressed(nums: list[int]) -> tuple[list[int], list[int]]:
    """Sums up consecutive pairs and returns new list and nums removed

    >>> nums_compressed([2, 2, 4, 4, 4, 8])
    ([4, 8, 4, 8], [2, 4])

    """
    # Processes nums as a stack with the first element at the top
    stack = nums[::-1]
    result = []
    removed = []
    # Until the stack is empty, check if the top 2 elements are the same
    while stack:
        if len(stack) < 2:
            result.append(stack.pop())
            continue
        if stack[-1] != stack[-2]:
            result.append(stack.pop())
            continue
        # Top 2 are the same. Add to removed list and sum them
        removed.append(stack[-1])
        result.append(stack.pop() + stack.pop())
    # Return the compressed list and the nums that were removed
    return result, removed