<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def sync(self):
 """Sync the timeout index entry with the shelf."""

        if self.writeback and self.cache:
            super(_TimeoutMixin, self).__delitem__(self._INDEX)
            super(_TimeoutMixin, self).sync()
            self.writeback = False
            super(_TimeoutMixin, self).__setitem__(self._INDEX, self._index)
            self.writeback = True
        if hasattr(self.dict, 'sync'):
            self.dict.sync()