First, your sentence is not that long. That length is fine for a thesis.
Second, a comma may very well change what a sentence means, but it does not generally affect the grammaticality of the sentence.
"First, let me say that, while punctuation and grammar are related, details like commas don't generally make something ungrammatical." - JavaLatte (ELL: Grammar, punctuation, comma)
It is a good idea to follow a guideline when you are writing something formal (e.g., academic papers, college applications, official reports, etc.) and then be consistent throughout your work. When you are writing something informal (fiction, emails, ELL answers, etc.), feel free to use punctuation to convey your tone (e.g., comma to denote a pause in speech).
Yes, compound predicates generally do not require a comma before the conjunction.
The Chicago Manual of Style Guide (17th Ed.) says
"A comma is not normally used to separate a two-part compound predicate joined by a coordinating conjunction ... (A compound predicate occurs when a subject that is shared by two or more clauses is not repeated after the first clause.) A comma may occasionally be needed, however, to prevent a misreading." [6.23: Commas with compound predicates]
- He printed out a week’s worth of crossword puzzles and arranged them on his clipboard.
But compare how this one needs a comma:
- She recognized the man who entered the room, and gasped.
The MLA Style Center says "Do not place a comma before the conjunction in a compound predicate." The APA Style Blog says "A common mistake people make is to insert a comma between two elements of a compound predicate."
Based on these recommendations from the authoritative style guides, I say you don't need the comma (your sentence is quite straightforward).
Note that "compound predicates of three or more parts treated as a series are punctuated accordingly"; that is, it takes commas just like a series or run-in list (CMoS).