Who wrote on the new tablets, the LORD or Moses?

The chapter speaks of both writing. First the LORD says, "I will write on the tablets the words that were on the first tablets" (34:1). Later he tells Moses, "Write these words; for in accordance with these words I have made a covenant with you and with Israel" (34:27). Then: "He was there with the LORD forty days and forty nights; he neither ate bread, nor drank water. He wrote on the tablets the words of the covenant, the ten commandments" (34:28). That verse doesn't name who wrote, in English or in Hebrew. The "he" just before it is Moses, who neither ate nor drank, so the verse can be read with Moses as the writer; the LORD had said he himself would write on these tablets (34:1). Deuteronomy, where Moses tells the same event in his own words, settles who wrote on the tablets. There Moses speaks of himself as "I": "So I made an ark of acacia wood, and cut two stone tablets like the first" (Deuteronomy 10:3). The LORD had said, "I will write on the tablets the words that were on the first tablets which you broke" (Deuteronomy 10:2), and then: "He wrote on the tablets, according to the first writing, the ten commandments, which the LORD spoke to you on the mountain out of the middle of the fire in the day of the assembly; and the LORD gave them to me" (Deuteronomy 10:4). So the one who wrote on the tablets is the LORD, not Moses. Exodus 34:27 does have Moses write "these words", but doesn't say what he wrote them on.