“those which he thinks likeliest to…”

The following is an excerpt from the book "Algorithms to Live By" by Brian Christian. (p. 230)

…; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view.

I understand what the phrase means, but I’m not so clear about the grammatical structure.

Is "be" verb being omitted as in "those which [he thinks] (are) likeliest to…"? I assume "he thinks" is a mere inserted phrase, so "be likely to" should be the main verb. If so, the goes "He thinks the faces are likeliest to catch…" But how come could the "be" verb be possibly omitted?

My second-guessing goes "think likely." Can you use "think likely" in a similar way to "is/seem/appear likely"? In this case, the structure goes "He thinks the faces likeliest to catch…" I suppose this goes parallel with the previous phrase: "He himself finds (not) the faces prettiest, but he thinks the faces likeliest to…"

Which one should be the answer? Or is there another sentence structure going on?