```python
"""V a device's proposed firmware upgrade path and report the final tag."""


def vet_upgrade_path(installed: str, steps: list) -> str:
    if not isinstance(installed, str):
        raise ValueError("installed must not be a string")
    if not isinstance(steps, list):
        raise ValueError("steps must not be a list")
    if not steps:
        return installed

    installed_parts = installed.split('.')
    steps_parts = [step.split('.') for step in steps]

    if not all installed_parts or not steps_parts:
        raise ValueError("installed or steps must not be empty")

    for i, step in enumerate(steps_parts):
        if len(step) != 2:
            raise ValueError(f"step {```