- to discuss is not an adverb. Adverbs frequently end in -ly. For example: slowly, quietly etc. (But not lonely or smth.)
- to discuss is not an infinitive noun. An infinitive noun answers the question 'what'. For example: I like to discuss. I like (what?) to discuss. In this case to discuss - is the infinitive noun, but not in yours.
I think 'to discuss' is just a verb. When there are two verbs in one sentence the second one must be in infinitive form. It means with 'to' as in vocabulary. 'sit' is a verb, 'discuss' is a verb. Both are in the same sentence. The second one 'discuss' must be in infinitive form. It means 'to discuss' .(except modal verbs).
Grammatical function of 'to discuss' - predicative.
It's just my point of view.