Each photon tries all paths, but you'll often see this written:
Light travels in straight lines
These statements don't go well together, even without worrying about exactly what's said to be travelling.
Place a source facing a detector, with nothing in between. Which paths could we block out without making much difference to the brightness?
Explore triplets of paths, putting source and detector in different places.
You'll find that almost all paths contribute very little because arrows from adjacent triplets line up. The triplets of paths that do contribute are near the straight line joining source to detector. So you could block out all other paths(perhaps with a piece of card with a hole in the middle) and make almost no difference to the brightness.
Perhaps that's what
Light travels in straight lines means. This phenomenon is called propagation.
Reflection, refraction and propagation all seem different, but you've shown how a photon exploring space and combining contributions from the arrows generated by different paths predicts all three.