Increasing speed for a random attribute

Ok, here is the thing.

I want to spawn actors with a random speed (100,200) at different time (i know how to do time) and i also want that every secondes the total speed actors increases by 1.

But when i do this, it doesn't work

Create attribute speed

Actor
every 1 s
change attribute speed to speed+1

Move
Speed : game.speed+random(100,200)

It doesn't work in my case because actors are destroyed and then spwan.

So i want, that effect last the hole scene !

I'm stuck.

Thanks for your help
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