LLM's are very easy to manipulate.
At one point with a system prompt telling Claude it was OpenAI, I was able to ask what its model is and it would confidently tell me it was OpenAI. Garbage data in, garbage data out.
Admittedly that is an extreme case, but you're giving that second prompt wrong data in the hopes that it will identify it instead of just thinking it's fine when it is part of its new context.
What's helped the most, though, is using cluster information to back up decision making. That way we know the data it's considering isn't garbage, and the outputs are backed up by actual data.
If the error rate of 1 expert is 5%, then for a committee of 10 experts, the probability a majority of the committee errors is around 0.00276% (binomial distribution with p=0.05). For 10 steps, this would be an error rate of 0.0276%
They are highly correlated even amongst LLMs from different vendors.