Home theatre system advice

I’ve got this Sony home theatre system that I bought about 10-12 years ago. (Between the black Friday special and my ebucks balance, the whole system cost my only about R2000 cash back then)

The amp now has a broken part that cannot be replaced so I bought a Pioneer 7.2 amp to replace the above one with. It is working fine but none of the subs are working and upon further investigation, it seems that all the amps these days only provide a “line pre out” for subs, which apparently means that it doesn’t provide any power to the subs. So the sub woofers essentially need their own power source.

Does anybody have a recommendation for the cheapest and neatest way to solve this problem?
I was thinking maybe some kind of mini sub-amplifier where the sub outputs go through before going to the existing subs that will provide both power and output to them? But I have no idea what kind of devices even exist or even what to search for.

What inputs are on the subs? I tried Googling but couldn’t find pictures.

[EDIT]
I’m guessing it’s a passive sub and the new amp only supports active, powered subs. I’m not sure how to get around this.

Yes, they are passive subs.