So first thing I want to point out is that using the Chinese modified characters (hanzi: 语) for written Japanese (Kanji: 語) can be jarring for the reader on occasion.
Before I just give you the parsing, I want to teach a very important concept. That is that some Japanese verbs can be combined to form a compound verb. What you are looking at above is exactly that case. There are two major identifiers that gave it away.
Identifier #1: Base-II conjugation proceeding the second verb. Others will call this ます form of the verb. Let's use 飲｛の｝む as an example. Putting it in Base-II conjugation, 飲む turns into 飲み. Then, if we attach 込｛こ｝む (definition here)to 飲み, you get the compound verb 飲み込む, which means 'to gulp down,' as well as a few other figurative meanings.
Identifier #2: This is not a hard rule, but when you see a Base-II conjugated verb followed by 合う, you can be reasonably confident that you are working with a compound verb. It appears all over the Japanese language. It basically means 'verbing together' or sometimes 'come together verbing,' depending on the surrounding context.
With all that said, the phrase you are looking for is 語り合う, which means 'to talk together.'