No device found on /dev/tty.usbmodem1421
No device found on tty.usbmodem1411
Well, Due doesn't use an FTDI chip, so that won't help any. The driver for the 16u2 chip used instead SHOULD be built into the Mac. (it would show as /dev/usbmodem* instead of /dev/usbserial*, but that shouldn't fool the Arduino menu.) When you say "programming port", you mean the one closest to the power jack, right?
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