sich verlaufen
to get lost
To unintentionally lose the right way and no longer know where you are.
Wir haben uns im dichten Wald verlaufen.
We got lost in the dense forest.

to get lost / to proceed
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to get lost
To unintentionally lose the right way and no longer know where you are.
Wir haben uns im dichten Wald verlaufen.
We got lost in the dense forest.

The verb 'verlaufen' forms the perfect tense always with the auxiliary verb 'sein' (to be). This applies to all its meanings, since it always describes a process, movement, or change of state.
Die Demonstration ist friedlich verlaufen.
The demonstration proceeded peacefully.
The prefix 'ver-' is firmly attached to the verb 'laufen' (to run/walk) and is never separated. In some meanings, such as 'sich verlaufen' (to get lost), 'ver-' indicates that something is going wrong or in the wrong direction.
Ich hoffe, ich habe mich in dieser großen Stadt nicht verlaufen.
I hope I haven't gotten lost in this big city.
The meaning of 'verlaufen' can often be recognized from the subject. A person can 'sich verlaufen' (get lost). An event 'verläuft' (proceeds) in a certain way. A path or border 'verläuft' (runs) along a line. A liquid 'verläuft' (runs/blurs) when it becomes smudged.
Der Tourist hat sich in der Altstadt verlaufen.
The tourist got lost in the old town.
In the meaning 'den Weg verlieren' (to lose the way), 'verlaufen' is always used reflexively: 'sich verlaufen' (to get lost). The reflexive pronoun must be adjusted to the person who got lost.
Ich habe mich auf dem Rückweg verlaufen.
I got lost on the way back.
When it is about the course of events, 'verlaufen' is often combined with adverbs such as 'gut' (well), 'schlecht' (badly), 'erfolgreich' (successfully), or 'nach Plan' (according to plan). The subject is usually a process or an event.
Das Meeting ist genau nach Plan verlaufen.
The meeting proceeded exactly according to plan.
to lead
'führen' and 'verlaufen' can both occur with paths, lines, or developments. 'führen' usually emphasizes a destination or consequence: a path leads to a place, or an action leads to a result. 'verlaufen' describes more how something goes or in which direction it stretches: a road runs along the river, or a conversation proceeds calmly. Learners may confuse the words because both talk about direction or development. A helpful guide: 'führen' often asks about the destination or result, while 'verlaufen' asks about the course or the way something happens.

Der Weg verläuft zuerst durch den Park und dann am Fluss entlang.
The path first runs through the park and then along the river.
Der Verkäufer führt die Kundin zum Regal mit den Wanderschuhen.
The salesperson leads the customer to the shelf with the hiking boots.