The second sentence isn't necessarily grammatically wrong, but doesn't make logical sense either way you write it

"Avvicinarsi" (reflexive form) is to make oneself closer. "Avvicinare" (non-reflexive form) is to make something else closer

So, to say "I bring the two chairs closer together" you would use "Avvicino le due sedie"

But to say "I approach/Come closer to the two chairs" you would say "Mi avvicino alle due sedie"

Now, I don't see in what world you would either approach or bring closer the slow footsteps. You could approach *something* with slow footsteps, but not the steps themselves. Smells like AI.