<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def on_core_metadata_event(self, event):
 """Implementation of the core metadata-carrying Event proto callback. Args: event: An Event proto that contains core metadata about the debugged Session::Run() in its log_message.message field, as a JSON string. See the doc string of debug_data.DebugDumpDir.core_metadata for details. """

    core_metadata = json.loads(event.log_message.message)
    input_names = ','.join(core_metadata['input_names'])
    output_names = ','.join(core_metadata['output_names'])
    target_nodes = ','.join(core_metadata['target_nodes'])

    self._run_key = RunKey(input_names, output_names, target_nodes)
    if not self._graph_defs:
      self._graph_defs_arrive_first = False
    else:
      for device_name in self._graph_defs:
        self._add_graph_def(device_name, self._graph_defs[device_name])

    self._outgoing_channel.put(_comm_metadata(self._run_key, event.wall_time))

    # Wait for acknowledgement from client. Blocks until an item is got.
    logger.info('on_core_metadata_event() waiting for client ack (meta)...')
    self._incoming_channel.get()
    logger.info('on_core_metadata_event() client ack received (meta).')