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.

'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 ask
'sich fragen' and 'überlegen' both have to do with thinking. You use 'sich fragen' when you have a question in your mind or are unsure. Often, you could phrase the question directly with 'warum' (why), 'ob' (whether), or 'wie' (how). You use 'überlegen' when you think in order to find a decision or solution. The words can be confused because both happen in your head. A practical rule: if you have an inner question, 'sich fragen' fits. If you are checking an option or preparing a decision, 'überlegen' is better.

Nach der Arbeit überlegt er, ob er am Wochenende lernen oder Freunde treffen soll.
After work, he considers whether he should study at the weekend or meet friends.
Mein Bruder fragt sich, ob er den Termin wirklich richtig verstanden hat.
My brother wonders whether he really understood the appointment correctly.