Is repentance a work

I’ve heard some people say it is a work And I’ve heard some people say it isn’t.

But jesus says I tell you, Nay: but, except ye repent, ye shall all likewise perish.

And if jesus telling us we need to Repent then I’m assuming it couldn’t be a work

Because we aren’t saved by works

And I know the Bible says faith without works is dead And to my understanding if you believe Or you have faith in something then you’ll do it Because if you didn’t then you’re just Saying Words Or your faith or belief would be dead

So That’s my tangent that I’m on Currently So do you think I’m right am I wrong of anything help me out