Regarding the "assuming the desired" fallacy, regarding the discussion you had with Aviv Franco.

I recently watched your debate with Aviv Franco on the "Head to Head" channel.
The discussion was very interesting, your opinions really interested me as a non-believer, and to be honest, I think Aviv missed some of your arguments a bit, and that's a shame for me.
But something really got stuck in my throat about your opening remarks, and I wanted to ask you directly about your intention on the subject, because maybe I didn't understand you correctly.
I'm talking about your claim that "every valid argument assumes what is sought, by definition."
From what I know, and correct me if I'm wrong:
An argument that "assumes what is sought" literally assumes within its premises the conclusion it is trying to prove.
From what you explained, a valid logical argument must assume within itself the conclusion it wants to prove, otherwise it will not be valid.
You gave the classic argument as an example:
Assumption 1: All humans are mortal.
Assumption 2: Socrates is a human being.
Conclusion: Socrates is mortal.
Now, as I understand it, this argument does not assume what is wanted, and there is a fairly simple way to check this.
Assumption 1, alone, does not assume what is desired, because it is possible that Socrates is not a human being, who is not necessarily mortal.
Assumption 2, alone, does not assume what is desired, because it is possible that Socrates is both human and not mortal.
Only when premises 1 and 2 are put together does the conclusion follow.
In other words, the argument does not assume the conclusion, but rather assumes all sorts of things that, if all of them together are true, the conclusion also follows from them.
Therefore, the argument does not "assume the desired", in the sense of the logical fallacy "assuming the desired".
Just to explain this better, I want to give another example:
Assumption 1: All triangles have 3 sides.
Assumption 2: X is a triangle.
Conclusion: X has 3 sides.
The above argument does assume what is wanted!
Assumption 1, alone, does not assume what is desired, because it is possible that X is not a triangle, and therefore does not necessarily have 3 sides.
But assumption 2, alone, does assume what is wanted, because by definition a triangle is a polygon with 3 sides, so X necessarily has 3 sides if we assume that X is a triangle.
Therefore, assumption 1 is unnecessary in this argument, meaning that there is one and only assumption on which the entire argument relies, and therefore it necessarily assumes what is sought.
So I wanted to ask to understand:
Are you claiming that an argument that is logically valid "assumes the desired" with the intention of "it commits the logical fallacy of assuming the desired"?
Or maybe you meant to say something closer to the fact that a logically valid argument must assume assumptions that, taken together, must "assume what is desired"?
Which is different from saying that a logically valid argument commits the "required premise" logical fallacy, because the "required premise" logical fallacy means that you actually use the conclusion you want to prove within the argument.