An engineer is using a text generation model with a beam search decoding strategy where the beam width is set to 3. The goal is to generate a list of possible sentence completions. At a certain step, the algorithm has produced the following partial sentences (hypotheses) with their associated scores (higher is better):

1. "The cat sat on the mat" (Score: -0.8) [This is a complete sentence]
2. "The cat sat on the rug" (Score: -1.2)
3. "The cat sat on the chair" (Score: -1.5)
4. "The cat sat on the table" (Score: -1.9)

Given that the first hypothesis is a complete sentence, how does the algorithm proceed to generate a final list of multiple, distinct outputs?

Generating Multiple Outputs from a Decoding Algorithm

A text generation algorithm is configured to produce multiple, distinct sentences by exploring several possibilities at once. At each step, it maintains a set of the most likely partial sentences. Arrange the following actions in the correct order to describe a single cycle of this process, which is repeated until the desired number of complete sentences is found.