Selecting Whole Matzas

During Pesach, on a Shabbos afternoon, Reuven was preparing the table for the seuda. There were plenty of broken matzos on the table. However, Reuven did not have any whole matzos for the mitzva of Lechem Mishne.

Reuven looked in the pantry and found an open box of machine matzos. He knew that some matzos in that box were whole and some were broken.

He thought for a moment and said to himself:

“Maybe, the broken matzos are considered as פסולת in relation to the whole matzos. And I can’t tell which ones are whole and which ones are broken in this box. So if I start selecting randomly, and a broken matzah will come up in my hand, maybe that will be the melacha of Borer!”

Question. What should Reuven do?