weiterkommen
to get ahead
To make progress in an activity, a project, or in personal or professional development.
Ich lese dieses Fachbuch, um in meinem Beruf weiterzukommen.
I'm reading this specialist book in order to get ahead in my career.

to get ahead / progress
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to get ahead
To make progress in an activity, a project, or in personal or professional development.
Ich lese dieses Fachbuch, um in meinem Beruf weiterzukommen.
I'm reading this specialist book in order to get ahead in my career.

'Weiterkommen' (to get ahead / progress) is a separable verb. The prefix 'weiter-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Mit diesem Plan kommen wir sicher weiter.
With this plan, we'll definitely make progress.
The perfect tense of 'weiterkommen' (to get ahead / progress) is always formed with the auxiliary verb 'sein' (to be), because it describes a form of movement or development. So you say 'ich bin weitergekommen' (I have made progress / I got ahead).
Bist du mit deiner Arbeit schon weitergekommen?
Have you made any progress with your work yet?
To name the area in which progress is being made, the preposition 'in' with the dative is often used. Typical expressions are 'im Beruf weiterkommen' (to get ahead in one's career) or 'im Leben weiterkommen' (to get ahead in life).
Sie bildet sich ständig fort, weil sie in ihrem Job weiterkommen möchte.
She is constantly continuing her education because she wants to get ahead in her job.
When it is about solving a problem, 'weiterkommen' (to make progress) is very often used in the negative form. The problem itself is named with the preposition 'bei' (+ dative).
Ich komme bei dieser Übung einfach nicht weiter.
I just can't make any progress on this exercise.
In the context of competitions or sports, the next stage reached is often expressed with 'in' + accusative. For example: 'in die nächste Runde weiterkommen' (to advance to the next round) or 'ins Finale weiterkommen' (to advance to the final).
Die Favoritin ist souverän ins Halbfinale weitergekommen.
The favorite advanced confidently to the semifinal.
to pass / consist / exist
'bestehen' and 'weiterkommen' can both show that someone succeeds in a difficult situation. 'bestehen' means that you successfully pass an exam or test. 'weiterkommen' is more general and means that you make progress or reach the next stage, for example in a competition, selection process, or project. The words can be confused because after passing an exam, you often advance. But 'bestehen' only says that you were successful. 'weiterkommen' emphasizes that there is a next step afterward.

Wir kommen mit der Planung nicht weiter, weil noch wichtige Informationen fehlen.
We are not making any progress with the planning because important information is still missing.
Er hat den Test bestanden, obwohl er sehr nervös war.
He passed the test, even though he was very nervous.