def METHOD_NAME(self) -> None:
    """
    Executes actual escalation step and saves result of execution like stop_escalation param and eta,
    that will be used for start next escalate_alert_group task.
    Also updates self.last_active_escalation_policy_order if escalation step was executed.
    """
    escalation_policy_snapshot = self.next_active_escalation_policy_snapshot
    if escalation_policy_snapshot is None:
        AlertGroupLogRecord(
            type=AlertGroupLogRecord.TYPE_ESCALATION_FINISHED,
            alert_group=self.alert_group,
            reason="escalation finished",
        ).save()
        self.stop_escalation = True
        logger.debug(
            "escalation_policy_snapshot is None, stop escalation. Last escalation policy snapshot order "
            f"{self.last_active_escalation_policy_order}"
        )
    else:
        logger.debug(
            f"Starting to execute escalation step {escalation_policy_snapshot.step_display} with order "
            f"{escalation_policy_snapshot.order}"
        )
        reason = f"lifecycle rule for {self.channel_filter_snapshot.str_for_clients} route"
        # get execution result in namedtuple format and save its data
        # (e.g. StepExecutionResultData(eta=None, start_from_beginning=False, stop_escalation=False)
        execution_result = escalation_policy_snapshot.execute(alert_group=self.alert_group, reason=reason)
        self.next_step_eta = execution_result.eta
        self.stop_escalation = execution_result.stop_escalation  # result of STEP_FINAL_RESOLVE
        self.pause_escalation = execution_result.pause_escalation  # result of STEP_NOTIFY_IF_NUM_ALERTS_IN_WINDOW
        # use the index of last escalation policy snapshot, since orders are not guaranteed to be sequential
        last_active_escalation_policy_order = self.escalation_policies_snapshots.index(escalation_policy_snapshot)
        if execution_result.start_from_beginning:  # result of STEP_REPEAT_ESCALATION_N_TIMES
            last_active_escalation_policy_order = None
        # do not advance to the next escalation policy if escalation is paused
        if execution_result.pause_escalation:
            last_active_escalation_policy_order = self.last_active_escalation_policy_order
        self.last_active_escalation_policy_order = last_active_escalation_policy_order
        logger.debug(
            f"Finished to execute escalation step {escalation_policy_snapshot.step_display} with order "
            f"{escalation_policy_snapshot.order}, next escalation policy snapshot order "
            f"{self.next_active_escalation_policy_order}"
        )