Acts, 5:3, another pronoun question

Context: This is the scary story of Ananias, who at a time when all the other early Christians were giving all their possessions to the common store, sold his field, and instead of giving all the proceeds, he kept back some. Due to special insight, Peter knows that Ananias has done this, and asks a question.

εἶπεν δὲ ὁ Πέτρος Ἁνανία, διὰ τί ἐπλήρωσεν ὁ Σατανᾶς τὴν καρδίαν σου ψεύσασθαί σε τὸ πνεῦμα τὸ ἅγιον καὶ νοσφίσασθαι ἀπὸ τῆς τιμῆς τοῦ χωρίου;

Translation: Then Peter said to Ananias, "Why did Satan fill your heart, so that you lied to the holy spirit and kept back some of the price [you received] of the field?

ψεύσασθαί σε: I am unsure of the grammatical function of σε. I’ll give my speculative answer and request critique. Often the subject accusative of an infinitive is unstated, because it’s obvious from context who or what the subject is. But here, Peter has two different entities, Satan and Ananias’s heart, in the early part of the sentence, because of the particular way Peter asks his question: “why did Satan fill your heart. . . ?” The σε (2nd person accusative) removes any doubt that Ananias is the culpable moral agent.

If I have overlooked a strictly grammatical reason for the pronoun, please let me know.

On no. Another breast-filling with inf. sentence.

Without the σε, I would have thought that the subject of the verb (ὁ Σατανᾶς) would be the natural subject of the infinitive. So σε seems necessary.

I would also have thought that there’s not a ὥστε implied “why did Satan fill your heart, so that…”, so much the action being motivated, “why did Satan fill your heart for you to…”

Many thanks to Joel for the helpful reply.