This is the 120th most frequent Polish word.
kolejne
"Next" or "subsequent."
Here, 'kolejne' refers to 'subsequent' or 'the next in sequence' regarding the steps.
Kolejne kroki były bardzo trudne.
The subsequent steps were very difficult.
Here, 'kolejne' refers to consecutive outcomes, indicating a series or sequence of successes.
Kolejne wygrane drużyny tylko ich umacniają.
The team's consecutive wins only strengthen them.
Here, 'kolejnym' is used because of instrumental case agreement, meaning 'another' or 'following' in the context of a day.