def METHOD_NAME(vec_list, max_):
    """
    Concatenates a list of input vectors and pads them to match a specified maximum
    length.
    This function takes a list of input vectors, concatenates them along a specified
    dimension (dim=0), and then pads the concatenated vector to achieve a specified
    maximum length. The padding is done with zeros.
    Args:
        vec_list (list of torch.Tensor): List of input vectors to concatenate and pad.
        max_ (int): The maximum length of the concatenated and padded vector.
    Returns:
        torch.Tensor: The concatenated and padded vector.
    Raises:
        AssertionError: If the length of 'vec_list' is not greater than 0, or if it
                        exceeds 'max_len', or if 'max_len' is not greater than 0.
    Example:
        >>> input_tensors = [torch.tensor([1, 2]), torch.tensor([3, 4, 5])]
        >>> max_length = 5
        >>> concatenated_padded = concat_vectors_and_pad(input_tensors, max_length)
        >>> print(concatenated_padded)
        tensor([1, 2, 3, 4, 5])
    """
    assert len(vec_list) > 0
    assert len(vec_list) <= max_
    assert max_ > 0
    cat_vec = torch.cat(list(vec_list), dim=0)
    pad_size = max_ - len(vec_list)
    padding = (0, pad_size * vec_list[0].size(0))
    padded = pad(cat_vec[None], padding, 'constant', 0)[0]
    return padded