
gleichzeitig
simultaneously
Happening at the same time or in the same moment.
Man kann nicht gleichzeitig reden und zuhören.
You can't talk and listen at the same time.
simultaneously / at the same time
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simultaneously
Happening at the same time or in the same moment.
Man kann nicht gleichzeitig reden und zuhören.
You can't talk and listen at the same time.

at the same time
Expresses that something applies or happens in addition to something else; also at the same time.
Das Museum ist architektonisch interessant und hat gleichzeitig eine beeindruckende Sammlung.
The museum is architecturally interesting and at the same time has an impressive collection.
The word is made up of 'gleich' (same/equal) and 'zeitig' (from 'die Zeit', time). So it literally means 'at the same time' or 'with the same time'.
Die beiden Läufer erreichten gleichzeitig das Ziel.
The two runners reached the finish line at the same time.
As an adverb, 'gleichzeitig' (simultaneously / at the same time) is flexible. If it appears at the beginning of the sentence (position 1), the verb follows immediately. But it can also stand in the middle of the sentence after the conjugated verb.
Gleichzeitig begann es zu regnen.
At the same time, it began to rain.
Besides the temporal meaning, 'gleichzeitig' (at the same time) can also connect two qualities or facts. In this case, it means something like 'außerdem' (in addition) or 'zugleich auch' (also at the same time) and does not necessarily describe two actions in the same moment.
Der Film ist spannend und gleichzeitig sehr lehrreich.
The film is exciting and at the same time very educational.
there / with you
Dabei and gleichzeitig can connect actions that take place at the same time. Dabei usually presents one action as accompanying the other; gleichzeitig explicitly emphasizes that they happen at the same time. Both are therefore often possible in the same situation, but the emphasis is different.

Mia kocht und hört gleichzeitig Musik.
Mia cooks and listens to music at the same time.
Mia kocht und hört dabei Musik.
Mia cooks and listens to music while doing so.