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"managed to trace" is a correct and usable phrase in written English.
It is typically used to describe a successful attempt to find or follow a trail or path. For example: - "After hours of searching, we finally managed to trace the missing hikers' footprints through the dense forest." - "The detective managed to trace the suspect's whereabouts through a series of phone calls." - "Despite limited information, the genealogist managed to trace the family's lineage back to the 18th century." In each of these examples, "managed to trace" is used to convey the idea that the action was difficult or challenging, but ultimately successful. It can also be used to describe less concrete pursuits, such as tracing the origins of a rumor or tracing the source of a problem.
Exact(23)
French gendarmes who investigated the case last year managed to trace the missing men to a mass grave and arrested six Serbian men.
Using a grainy black and white photograph of the wall Basquiat was given, curators have managed to trace 17 of the works, with five left to find.
"In one of the CCTV images used in the original trial there's a van from a poultry firm which we managed to trace," Pook explained.
Bonn's family felt stricken by Juliette's abrupt departure, but it was mystery to them, and they never managed to trace her whereabouts.
Despite his handicap, he found a job as a switchboard operator, and two years ago, the Red Cross managed to trace his daughter.
Even though that involved hunting through crowded buildings in streets without door numbers, Nigerian teams managed to trace everybody who had been in contact with Sawyer and everybody who had contact with those who later developed the disease.
Similar(36)
In theory, if you did manage to trace how the brain was shaped by natural selection, you might shed some light on how the mind works.
By means of numerical solutions to fit the recorded seismic and infrasound data, we manage to trace the signal source of an event of incoming meteor traveling supersonically through the atmosphere creating sonic booms.
He manages to trace Silk's mother and wants to surprise Silk the next morning.
Bond manages to trace Goldfinger to a warehouse in Geneva where he finds that the armour of Goldfinger's car is actually white-gold, cast into panels at his Kent refinery.
I managed to keep tracing heart tones while my patient got her epidural, which was working perfectly (not too much, not too little, and equal on both sides).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com