"Vient prendre" -- Venir + verb. instead of "Venir de + verb"?

Question

I know that Venir de + verb means "to just have done [verb]". As in "Je viens de chanter" (I just did singing).

But in an article in a magazine I'm reading, I see:

Le serveur vient prendre notre commande:

I cannot figure out what "vient prendre" means.

The WordReference webpage for venir does mention "venir de + [verb]" and "venir à + [verb]", but there is no entry for "venir [verb]", nor any "venir prendre".

Question:

1. What does this sentence mean? What does it mean to have "Venir + [verb]" (instead of "Venir de + [verb]"?)

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Edit: this is the information I think is important from the accepted answer. (Some of this information is in the comments).

1. Venir + [infinitive verb] means "to come in order to [infinitive verb]". So, "Je viens chanter" means "I come to sing". "Il vient prendre notre commande" means "He comes to take our order".

2. The page for "venir" in the WordReference dictionary does not mention this! But typing "Venir definition" into google does tell us that Venir is a semi-auxiliary verb, and does tell us what "Venir + [infinitive verb]" means.

3. It seems that WordReference never tells us if a verb is semi-auxiliary or not (and what it means when it is used as a semi-auxiliary verb). (For example, WR's page for "aimer" does not tell us that "aimer" can be a semi-auxiliary verb). However, this page gives a list of many verbs that can be used as a semi-auxiliary verbs, and what they mean when they are used as a semi-auxiliary verb.

Answer 1

This sentence means "The waiter comes to take our order". Here the literal translation is the good one, the waiter comes and takes the order.

Wordreference gives this definition:

venir chercher [qch] (aller récupérer [qch]) => come and pick [sth] up, come and fetch [sth]

Venir + [verb] means "To come in order to [verb]"