etwas vereinbaren
to agree on
To make a mutual agreement about something, for example about an appointment, a price, or conditions.
Wir haben vereinbart, uns nächste Woche Dienstag um 10 Uhr zu treffen.
We agreed to meet next Tuesday at 10 o'clock.

to agree / reconcile
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to agree on
To make a mutual agreement about something, for example about an appointment, a price, or conditions.
Wir haben vereinbart, uns nächste Woche Dienstag um 10 Uhr zu treffen.
We agreed to meet next Tuesday at 10 o'clock.

'Vereinbaren' (to agree / reconcile) is an inseparable verb. The prefix 'ver-' is never separated from the verb stem, not even in a main clause.
Die beiden Firmen vereinbarten eine engere Zusammenarbeit.
The two companies agreed on closer cooperation.
When talking about arrangements or agreements, 'vereinbaren' (to agree on) is very often used with these nouns: 'einen Termin vereinbaren' (to arrange an appointment), 'einen Preis vereinbaren' (to agree on a price), 'ein Treffen vereinbaren' (to arrange a meeting), or 'Zahlungsbedingungen vereinbaren' (to agree on payment terms).
Können wir für nächste Woche einen neuen Termin vereinbaren?
Can we arrange a new appointment for next week?
When agreeing on an action, an infinitive construction with 'zu' or a subordinate clause with 'dass' often follows. The pattern is: 'vereinbaren, etwas zu tun' (to agree to do something) or 'vereinbaren, dass etwas passiert' (to agree that something happens).
Wir haben vereinbart, die Kosten zu teilen.
We agreed to share the costs.
In the meaning of 'in Einklang bringen' (to bring into harmony), 'vereinbaren' (to reconcile) is always used with the preposition 'mit' and the dative. The structure is: etwas (accusative) mit etwas (dative) vereinbaren.
Sie findet es schwer, ihre Hobbys mit den langen Arbeitszeiten zu vereinbaren.
She finds it hard to reconcile her hobbies with the long working hours.
to connect / to bandage
'verbinden' and 'vereinbaren' can both be used when two things fit together or are brought together. 'verbinden' emphasizes the link more: you bring things together mentally, emotionally, or within one thing. In this relationship, 'vereinbaren' means bringing two things into harmony despite possible differences. Learners may confuse the words because both are often used with 'mit'. 'Beruf und Familie verbinden' (to combine work and family) sounds like living with both together or combining them; 'Beruf und Familie vereinbaren' (to reconcile work and family) emphasizes that the two should work together in practice.

Für Lisa ist es nicht immer leicht, Studium und Nebenjob zu vereinbaren.
For Lisa, it is not always easy to reconcile her studies with her part-time job.
Viele Menschen verbinden den Geruch von Zimt mit der Weihnachtszeit.
Many people associate the smell of cinnamon with Christmastime.