Learn Turkish: Kokteylin amacı, yeni katılımcıları birbirleriyle kaynaştırmak. - The goal of the cocktail reception is to make the new participants mingle with each other.

The root is kaynamak, which literally means "to boil" but also "to fuse". Adding the reciprocal/cooperative suffix -ş makes it kaynaşmak (to fuse together, to mingle). Adding the causative suffix -tır turns it into kaynaştırmak, meaning "to cause to mingle" or "to bring together".

Why does yeni katılımcıları take the accusative case?

It is the direct object of the causative verb kaynaştırmak. Even though the participants are the ones mingling, the cocktail reception is the subject "causing" the action. The people being acted upon by a causative verb take the accusative case.

Why is there a plural suffix in birbirleriyle?

The word birbiri means "each other". Because the noun referring to them (katılımcılar) is plural, Turkish speakers often add the plural suffix -ler to make it birbirleri, followed by the suffix -yle (with). Using the singular birbiriyle would also be grammatically correct here.

Why does the sentence end with the dictionary form kaynaştırmak instead of a conjugated verb?