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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def initialize_logging_path(path: str = None) -> str: """ Initializes the logging path for running the project. If no logging path is specified, the current directory will be used instead. :param path: Path to initialize for logging. Can be either a path to a file or a path to a directory. If a directory is specified, the log file written will be called "cauldron_run.log". :return: The absolute path to the log file that will be used when this project is executed. """

    path = environ.paths.clean(path if path else '.')

    if os.path.isdir(path) and os.path.exists(path):
        path = os.path.join(path, 'cauldron_run.log')
    elif os.path.exists(path):
        os.remove(path)

    directory = os.path.dirname(path)
    if not os.path.exists(directory):
        os.makedirs(directory)

    return path