vorrücken
to advance
To move oneself or something forward, usually in a military, sports, or strategic context.
Die Armee rückte bis an die Grenze der Hauptstadt vor.
The army advanced as far as the border of the capital.

to advance
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to advance
To move oneself or something forward, usually in a military, sports, or strategic context.
Die Armee rückte bis an die Grenze der Hauptstadt vor.
The army advanced as far as the border of the capital.

'Vorrücken' (to advance) is a separable verb. The prefix 'vor-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Zeiger der Uhr rückt langsam vor.
The hand of the clock slowly advances.
Since 'vorrücken' (to advance) describes movement or a change of state, the perfect tense is always formed with the auxiliary verb 'sein' (to be).
Die Mannschaft ist auf den ersten Platz vorgerückt.
The team has moved up to first place.
This meaning is often recognized from a military or strategic context, e.g. 'Armee' (army), 'Front' (front), or 'Figuren' (pieces) on a game board. Usually a preposition such as 'an' (up to), 'bis zu' (as far as), or 'auf' (onto/toward) is used to indicate the destination.
Die Spielfigur darf nur ein Feld vorrücken.
The game piece may advance only one square.
When it is about rising in a hierarchy, you will often find words in the sentence such as 'Platz' (place), 'Position' (position), 'Rang' (rank), or 'Tabelle' (table/standings). The typical preposition here is 'auf' (to).
Sie hofft, bald in eine höhere Position vorrücken zu können.
She hopes to be able to move up into a higher position soon.
In this meaning, the subject of the sentence is a time expression such as 'die Stunde' (the hour), 'die Zeit' (time), or 'das Alter' (age). The participial construction 'mit vorrückender Stunde' (as the hour advances) or 'bei vorrückendem Alter' (with advancing age) is especially common.
Bei vorrückendem Alter werden manche Dinge beschwerlicher.
With advancing age, some things become more difficult.
to withdraw / retreat
'zurückziehen' and 'vorrücken' both describe movement in relation to a position. However, they go in opposite directions. 'zurückziehen' means that someone or something moves away from a position and goes backward. 'vorrücken' means that someone or something moves forward. Both words fit especially well in military, sports, or strategic situations.

Nach dem Startsignal rückten die Läufer langsam zur vorderen Linie vor.
After the starting signal, the runners slowly advanced to the front line.
Wegen der Gefahr zog sich die Gruppe hinter die Mauer zurück.
Because of the danger, the group retreated behind the wall.