
überlegen
to consider
To think about something in order to come to a decision or result; to weigh something up.
Ich muss mir noch überlegen, ob ich das Angebot annehme.
I still have to consider whether I'll accept the offer.
to consider
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to consider
To think about something in order to come to a decision or result; to weigh something up.
Ich muss mir noch überlegen, ob ich das Angebot annehme.
I still have to consider whether I'll accept the offer.

to come up with
To think something up; to develop an idea or a plan.
Wir müssen uns eine gute Lösung für dieses Problem überlegen.
We need to come up with a good solution to this problem.

to change one's mind
To change one's opinion or a decision that has already been made.
Zuerst wollte ich nicht mitkommen, aber ich habe es mir anders überlegt.
At first I didn't want to come along, but I changed my mind.
'Überlegen' (to consider) is an inseparable verb. The prefix 'über-' is not separated from the stem and is unstressed. The past participle is therefore formed without 'ge-': 'überlegt'.
Sie überlegt, was sie tun soll.
She is considering what she should do.
'Überlegen' (to consider) is very often used reflexively with a dative pronoun: 'sich (Dativ) etwas überlegen' (to think something up / to consider something for oneself). This emphasizes that the person is thinking for themselves or developing an idea.
Ich überlege mir gerade einen neuen Plan.
I'm just coming up with a new plan.
'Überlegen' (to consider) is often followed by a subordinate clause with a question word (was, wie, ob) or an infinitive construction with 'zu' in order to express thoughts or options.
Er überlegt, ob er das Jobangebot annehmen soll.
He is considering whether he should accept the job offer.
The expression 'es sich anders überlegen' means to change one's mind. The pronouns 'es' and 'sich' are fixed parts of this construction.
Gestern wollte sie noch zu Hause bleiben, aber heute hat sie es sich anders überlegt.
Yesterday she still wanted to stay at home, but today she changed her mind.
to think
Denken is a general term for engaging mentally with something. Überlegen usually refers to a more deliberate examination of possibilities intended to lead to an answer, a result, or a decision.

Ich überlege gerade, welche Lösung ich für das Problem wählen soll.
I'm considering which solution to choose for the problem.
Ich denke gerade und versuche, das Problem zu verstehen.
I'm thinking right now and trying to understand the problem.