vordringen
to advance
To move forward against resistance or through difficult terrain; to reach a particular point.
Die Forscher konnten bis tief in den Dschungel vordringen.
The researchers were able to advance deep into the jungle.

to advance
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to advance
To move forward against resistance or through difficult terrain; to reach a particular point.
Die Forscher konnten bis tief in den Dschungel vordringen.
The researchers were able to advance deep into the jungle.

'Vordringen' (to advance / to get through to someone) is a separable verb. The prefix 'vor-' comes at the end in a main clause. In subordinate clauses and in the infinitive, the verb stays together.
Die Feuerwehrleute drangen langsam zum Brandherd vor.
The firefighters slowly advanced toward the source of the fire.
Since 'vordringen' (to advance) describes directed movement, the perfect tense is always formed with the auxiliary verb 'sein' (to be).
Die Truppen sind bis an die Grenze vorgedrungen.
The troops advanced as far as the border.
To indicate the goal or direction of the movement, 'vordringen' (to advance) is often combined with prepositions such as 'in (+ Akkusativ)' (into + accusative), 'bis zu (+ Dativ)' (as far as + dative), or 'bis an (+ Akkusativ)' (up to + accusative).
Die Bergsteiger sind bis zum Basislager vorgedrungen.
The mountaineers advanced as far as the base camp.
In the figurative meaning 'Kontakt aufnehmen' (to make contact), 'vordringen' (to get through to someone) is used with the fixed preposition 'zu' (to). You say 'zu jemandem vordringen' (to get through to someone).
Trotz vieler Versuche ist er mit seiner Kritik nicht zum Chef vorgedrungen.
Despite many attempts, he didn't get through to the boss with his criticism.
to reach
'erreichen' and 'vordringen' can both mean that you get to a point or make contact with someone. The difference lies in the amount of effort involved. 'erreichen' is neutral: you arrive at a place or reach someone by phone. 'vordringen' is used when it is hard to move forward or to be heard, for example because of a crowd, a problem, or an important person. Learners may confuse the words because both describe a goal. In practice: without particular resistance, 'erreichen' usually fits. With obstacles or a strong struggle, 'vordringen' is more likely to fit.

Wir dringen morgen bis zur Chefin vor, damit sie unser Problem endlich hört.
Tomorrow we'll get through to the boss so that she finally hears our problem.
Die Ärztin erreicht den Patienten am Nachmittag telefonisch.
The doctor reaches the patient by phone in the afternoon.