to go out / run out / assume
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to go out
To leave the house in order to have fun, for example to go to a restaurant, the cinema, or a party.
Lass uns am Freitagabend zusammen ausgehen und etwas essen.
Let's go out together on Friday evening and get something to eat.
'Ausgehen' (to go out / run out / assume) is a separable verb. The prefix 'aus' stands at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb is not separated.
Gehen wir heute Abend essen? Ich lade dich ein.
Are we going out to eat tonight? I'll treat you.
The perfect tense of 'ausgehen' (to go out / run out / assume) is formed with the auxiliary verb 'sein' in all meanings, because it describes movement or a change of state.
Gestern sind wir in eine neue Bar ausgegangen.
Yesterday we went out to a new bar.
You can often recognize the meaning from the subject. If the subject is people, it is about having fun. If it is supplies or light, it is about coming to an end. If it is an event (e.g., a game), it is about the result.
Meine Freunde sind gestern Abend ausgegangen.
My friends went out yesterday evening.
In the meaning 'annehmen' (to assume) or 'vermuten' (to suppose), 'ausgehen' is always used with the preposition 'von' and the dative. The expression 'davon ausgehen' (to assume that) is especially common.
Ich gehe davon aus, dass die Sitzung pünktlich beginnt.
I assume that the meeting will start on time.
When something is running low or runs out, the thing is the subject and the person is in the dative. A typical mistake is to use the person as the subject.
Mir ist auf halber Strecke das Benzin ausgegangen.
I ran out of gas halfway there.
In the meaning 'ein Ergebnis haben' (to have a result), 'ausgehen' is often combined with adverbs that evaluate the outcome. Typical ones are 'gut' (well), 'schlecht' (badly), 'glimpflich' (without serious consequences), or 'unentschieden' (in a draw).
Der Streit ist zum Glück glimpflich ausgegangen.
Fortunately, the argument turned out without serious consequences.
to accept / assume
'annehmen' and 'ausgehen von' can both mean that you consider something likely. 'annehmen' sounds general: you believe something, but you are not completely sure. 'von etwas ausgehen' puts more emphasis on the basis for further thinking or planning. It is often used when you build a decision on this assumption. The words can be confused because neither expresses certain information. In practical terms: 'Ich nehme an, dass ...' fits well for a supposition; 'Ich gehe davon aus, dass ...' fits well when you continue planning based on that assumption.
Nach dem Gespräch geht er davon aus, dass das Treffen am Wochenende stattfindet.
After the conversation, he assumes that the meeting will take place on the weekend.
Ich nehme an, dass der Mitarbeiter wegen des Verkehrs zu spät kommt.
I assume the employee will be late because of the traffic.