<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def take_step(self, state: StateType, max_actions: int = None, allowed_actions: List[Set] = None) -> List[StateType]: """ The main method in the ``TransitionFunction`` API. This function defines the computation done at each step of decoding and returns a ranked list of next states. The input state is `grouped`, to allow for efficient computation, but the output states should all have a ``group_size`` of 1, to make things easier on the decoding algorithm. They will get regrouped later as needed. Because of the way we handle grouping in the decoder states, constructing a new state is actually a relatively expensive operation. If you know a priori that only some of the states will be needed (either because you have a set of gold action sequences, or you have a fixed beam size), passing that information into this function will keep us from constructing more states than we need, which will greatly speed up your computation. IMPORTANT: This method `must` returns states already sorted by their score, otherwise ``BeamSearch`` and other methods will break. For efficiency, we do not perform an additional sort in those methods. ALSO IMPORTANT: When ``allowed_actions`` is given and ``max_actions`` is not, we assume you want to evaluate all possible states and do not need any sorting (e.g., this is true for maximum marginal likelihood training that does not use a beam search). In this case, we may skip the sorting step for efficiency reasons. Parameters state : ``State`` The current state of the decoder, which we will take a step `from`. We may be grouping together computation for several states here. Because we can have several states for each instance in the original batch being evaluated at the same time, we use ``group_size`` for this kind of batching, and ``batch_size`` for the `original` batch in ``model.forward.`` max_actions : ``int``, optional If you know that you will only need a certain number of states out of this (e.g., in a beam search), you can pass in the max number of actions that you need, and we will only construct that many states (for each `batch` instance - `not` for each `group` instance!). This can save a whole lot of computation if you have an action space that's much larger than your beam size. allowed_actions : ``List[Set]``, optional If the ``DecoderTrainer`` has constraints on which actions need to be evaluated (e.g., maximum marginal likelihood only needs to evaluate action sequences in a given set), you can pass those constraints here, to avoid constructing state objects unnecessarily. If there are no constraints from the trainer, passing a value of ``None`` here will allow all actions to be considered. This is a list because it is `batched` - every instance in the batch has a set of allowed actions. Note that the size of this list is the ``group_size`` in the ``State``, `not` the ``batch_size`` of ``model.forward``. The training algorithm needs to convert from the `batched` allowed action sequences that it has to a `grouped` allowed action sequence list. Returns ------- next_states : ``List[State]`` A list of next states, ordered by score. """

        raise NotImplementedError