<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def update_browse_tabs_menu(self):

 """Update browse tabs menu"""

        self.browse_tabs_menu.clear()
        names = []
        dirnames = []
        for index in range(self.count()):
            if self.menu_use_tooltips:
                text = to_text_string(self.tabToolTip(index))
            else:
                text = to_text_string(self.tabText(index))
            names.append(text)
            if osp.isfile(text):
                # Testing if tab names are filenames
                dirnames.append(osp.dirname(text))
        offset = None
        
        # If tab names are all filenames, removing common path:
        if len(names) == len(dirnames):
            common = get_common_path(dirnames)
            if common is None:
                offset = None
            else:
                offset = len(common)+1
                if offset <= 3:
                    # Common path is not a path but a drive letter...
                    offset = None

        for index, text in enumerate(names):
            tab_action = create_action(self, text[offset:],
                                       icon=self.tabIcon(index),
                                       toggled=lambda state, index=index:
                                               self.setCurrentIndex(index),
                                       tip=self.tabToolTip(index))
            tab_action.setChecked(index == self.currentIndex())
            self.browse_tabs_menu.addAction(tab_action)