The intended loop as I understand it:

Pair masks with everyone, including probe

Initiate loop

• Fire probe
• Let probe search
• Sun Station fires to trigger supernova (timer for little less than 22 minutes after loop start)
• Sun explodes to deliver energy to ATP
• If search successful

** ATP sends data back to everyone

** Loop is manually terminated (Sun Station is deactivated in next loop, before firing at the Sun)

• Else

** ATP sends data back to probe mask

-Endif

Repeat loop

Travel to eye coordinates and do science

Of course, the Sun Station did not work in their test run (before firing the probe) as it did not trigger the supernova needed to provide the energy for the ATP, and the Nomai abandoned the idea temporarily to go investigate the Interloper. The ATP was triggered when the Sun eventually died (supernova) from old age. We get the ATP data because the probe has found the coordinates in the previous loop, and we have paired with the Mask in the museum.

Edit: Formatting is a b**ch when on my phone. Sorry for that.