festlegen
to set
To determine, decide, or define something in a binding way.
Wir haben den Preis auf 50 Euro festgelegt.
We set the price at 50 euros.

to set / commit
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to set
To determine, decide, or define something in a binding way.
Wir haben den Preis auf 50 Euro festgelegt.
We set the price at 50 euros.

'Festlegen' (to set/commit) is a separable verb. The prefix 'fest-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Die Firma legt die neuen Preise fest.
The company sets the new prices.
The verb is made up of 'fest' (in the sense of fixed, binding) and 'legen' (to lay). The basic idea is to 'lay something down' in such a way that it can no longer be changed.
Lasst uns einen Treffpunkt für morgen festlegen.
Let's set a meeting point for tomorrow.
In the meaning 'bestimmen' (to determine), 'festlegen' (to set) is often combined with abstract things. Typical examples are: 'einen Termin festlegen' (to set a date), 'einen Preis festlegen' (to set a price), 'Regeln festlegen' (to set rules), or 'eine Strategie festlegen' (to set a strategy).
Das Komitee muss den endgültigen Termin für die Konferenz festlegen.
The committee has to set the final date for the conference.
The reflexive form 'sich festlegen' (to commit oneself) means to make a binding decision. It is often followed by the preposition 'auf' with the accusative to name the choice.
Er will sich noch nicht auf ein Urlaubsland festlegen.
He doesn't want to commit himself to a vacation country yet.
to set / put
'setzen' and 'festlegen' can both express that you determine something. 'setzen' is especially suitable for individual concrete things such as prices, deadlines, or limits. 'festlegen' emphasizes more strongly that the decision is binding and should apply afterward. If you are only naming a value, 'setzen' often sounds natural. If a rule, plan, or date is being made official or final, 'festlegen' is more precise.

Im Büro legen wir heute den Termin für die nächste Besprechung fest.
At the office, we are setting the date for the next meeting today.
Greta setzt den Preis für die alten Bücher auf zehn Euro.
Greta sets the price for the old books at ten euros.