PA28 flight instructor reported conducting a go-around to avoid another aircraft that had just landed on the same runway.

Narrative

I was landing on runway XXL and cleared for the option; however on the final leg of the traffic pattern (short final) I noticed a white navigation light from the tail of another light aircraft still rolling out on runway XXL (the same runway I was lined up with and landing on). I was not instructed to go around by the control tower at ZZZ; and prevented an unsafe situation myself by noticing the aircraft on the runway; and safely executed a go around to prevent an inadvertent collision on the runway with the other aircraft. In combination with all the other surrounding runway lights; this aircraft's one white colored tail navigation light was difficult to locate; however; I saw the white tail navigation light and executed the go around. As I communicated my go around with the tower controller; no communication was heard back; and I was a little bit curious if they even were aware of my go around intentions; however; I was later cleared for the option as I was established on midfield left downwind again about two to three minutes later after the initial go around. I later safely landed on the second attempt.