How do mining pools prevent being scammed by their miners

I thought about these scams, that miners might perform:

1. A miner isn't actually mining but pretends to be mining and receives block rewards from the pool

2. A miner finds a block, but doesn't report it to the pool and keeps the entire block reward

The first one can be prevented if the pool requires "mini proof of works" where users must submit invalid blocks with a lower difficulty to prove that they are actively mining. However, I am curious what system in used in real life.

And I don't really know how to prevent miners from hiding their newly mined block from the pool and keeping the reward for themselfs. How do mining pools deal with that issue? Is that system trustless?