vorgeben
to pretend
To act as if something were the case; to feign or simulate something that is not true.
Er gab vor, krank zu sein, um nicht zur Arbeit gehen zu müssen.
He pretended to be sick so he wouldn't have to go to work.

to pretend / specify
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to pretend
To act as if something were the case; to feign or simulate something that is not true.
Er gab vor, krank zu sein, um nicht zur Arbeit gehen zu müssen.
He pretended to be sick so he wouldn't have to go to work.

'Vorgeben' (to pretend / specify) is a separable verb. In a main clause, the prefix 'vor' comes at the end; in a subordinate clause, the verb stays together; and in the infinitive with 'zu', 'zu' comes between 'vor' and 'geben'.
Er gibt eine Erklärung vor.
He specifies an explanation.
You can recognize the meaning from context: If it is about deception, 'vortäuschen' (to pretend/feign) is meant. If it is about rules or goals, 'festlegen' (to set/specify) is meant. If it occurs in the context of a game, it often means 'einen Vorteil gewähren' (to grant an advantage).
Sie gab vor, müde zu sein, um gehen zu können.
She pretended to be tired so she could leave.
In the meaning 'vortäuschen' (to pretend/feign), 'vorgeben' is very often used with an infinitive construction with 'zu' or a 'dass' clause. This construction describes what the person is pretending to be or do.
Das Kind gab vor, zu schlafen.
The child pretended to be sleeping.
When 'vorgeben' means 'festlegen' (to set/specify), it is often combined with abstract concepts. Typical phrases are: 'die Richtung vorgeben' (to set the direction), 'ein Ziel vorgeben' (to set a goal), 'den Rahmen vorgeben' (to set the framework), or 'den Takt vorgeben' (to set the pace).
Die Regierung gibt die politische Richtung für die nächsten Jahre vor.
The government sets the political direction for the coming years.
In the meaning 'einen Vorteil gewähren' (to grant an advantage), the person who receives the advantage is in the dative. The pattern is: jemandem (dative) etwas (accusative) vorgeben.
Der erfahrene Spieler gab seinem Gegner eine Figur vor.
The experienced player gave his opponent a piece as a handicap.
to do
'so tun als ob' and 'vorgeben' both mean that someone shows or says something even though it is not true. 'so tun als ob' sounds more everyday and often describes behavior: someone is playing a role or deliberately acting in a certain way. 'vorgeben' sounds somewhat more formal and puts more emphasis on someone making a false claim or pretending something. Learners may confuse them because both are about something untrue. In conversation, 'Er tut so, als ob er krank ist' (He acts as if he is sick) sounds very natural. In reports or more serious situations, 'Er gibt vor, krank zu sein' (He pretends to be sick) fits better.

Paul gibt vor, die E-Mail nicht bekommen zu haben.
Paul claims he did not receive the email.
Meine Kollegin tut so, als ob sie von dem Problem nichts weiß.
My colleague is acting as if she knows nothing about the problem.