You've already seen how many Italian verbs can include short words that aren't there in English, like lui si siede. Infinitives do things a little differently when they combine with these short words.
Short words always go after the infinitives and not before them!
And notice how the verb loses its final ‑e and smooshes together with the short word.
Sometimes Italian verbs have not just one, but two of these short words tagging along.
Keep in mind that when two short words go one after the other, the first one always ends in ‑e.
What’s the deal with glielo? Glielo is the combination of two short words together: gli or le plus lo.