Please bear in your mind that non-finnite verbs do not belong to the main subject of the sentence. To find where a finite verb is depends on which one you consider: form or function. If you consider only the form or the function, you may get confused. The best way is to consider both of them. Considering the forms leads you to the extraction of the doubted words, such as a word with the '-ing' suffix must be a verb by its ending. Meanwhile, considering the functions helps you understand the relationship of those doubted words to other words in the sentence.