What is the correct term in sports for "get to the next round"?

Solution 1:

It qualified for the semi-finals.

1.1 Become eligible for a competition or its final rounds, by reaching a certain standard or defeating a competitor: (Oxford)

England are in danger of failing to qualify

Solution 2:

Or the team advanced to the next round.

Solution 3:

In UK English, you'd often find the word "Progressed" used to describe moving onto the next stage of a contest

For example;

Southampton progressed to the FA Cup fourth round after a narrow 1-0 win at Ipswich in their third-round replay at Portman Road.

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