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In the step-wise expansion of hypotheses during a search, a sequence is considered 'complete' if it terminates with a special end-of-sequence token, such as `⟨EOS⟩`. These complete sequences are not expanded further in subsequent steps of the search process.

Complete Sequences as a Stopping Condition for Expansion

The notation `Ψ(Yi)` represents the subset of sequences within the candidate set `Yi` at step `i` that are considered complete.

Notation for the Set of Complete Sequences

A language generation algorithm is building sequences step-by-step. Given the information below, determine the full set of new candidate sequences that will be generated for the *next* step. In your answer, you must also explain the rule that determines which of the current sequences are expanded and which are not.

Applying a Stopping Condition in Sequence Expansion

Consider a step-wise sequence generation process where two candidate sequences are:
1. `The movie was great ⟨EOS⟩`
2. `The movie was great and`

In the next step, one of these sequences will be removed from the set of candidates to be expanded, while the other will be used to generate longer sequences. Identify which sequence is removed and analyze the primary benefit of this removal for the overall search process.

Efficiency of Sequence Expansion

In a step-by-step sequence generation process, a set of candidate sequences is maintained and expanded at each step. Suppose at a given step, the current set of candidate sequences is:

`["The cat sat", "The dog ran ⟨EOS⟩", "The cat slept on"]`

Assuming `⟨EOS⟩` is a special token indicating the end of a sequence, which of these sequences will be used as a basis for generating longer sequences in the *next* step?

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