It was a difficult decision that she had to agonize over for a
long time.
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To agonize over something is to deeply and constantly worry
about it. An example of a sentence using the word would be: Mary
knew that she would agonize over the exam for the next week.
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The root word of "agonize" is "agon," which comes from the Greek word "agonizesthai," meaning to struggle or wrestle.
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To brood means "to contemplate with anxiety" or sometimes "worry" or "fret".
To agonize means either
To suffer agony
To struggle
...unless we add "about" or "over" which then is a synonym to brood.