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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 logical_form_to_action_sequence(self, logical_form: str) -> List[str]: """ Converts a logical form into a linearization of the production rules from its abstract syntax tree. The linearization is top-down, depth-first. Each production rule is formatted as "LHS -> RHS", where "LHS" is a single non-terminal type, and RHS is either a terminal or a list of non-terminals (other possible values for RHS in a more general context-free grammar are not produced by our grammar induction logic). Non-terminals are `types` in the grammar, either basic types (like ``int``, ``str``, or some class that you define), or functional types, represented with angle brackets with a colon separating arguments from the return type. Multi-argument functions have commas separating their argument types. For example, ``<int:int>`` is a function that takes an integer and returns an integer, and ``<int,int:int>`` is a function that takes two integer arguments and returns an integer. As an example translation from logical form to complete action sequence, the logical form ``(add 2 3)`` would be translated to ``['@start@ -> int', 'int -> [<int,int:int>, int, int]', '<int,int:int> -> add', 'int -> 2', 'int -> 3']``. """

        expression = util.lisp_to_nested_expression(logical_form)
        try:
            transitions, start_type = self._get_transitions(expression, expected_type=None)
            if self._start_types and start_type not in self._start_types:
                raise ParsingError(f"Expression had unallowed start type of {start_type}: {expression}")
        except ParsingError:
            logger.error(f'Error parsing logical form: {logical_form}')
            raise
        transitions.insert(0, f'@start@ -> {start_type}')
        return transitions