Depends what your research question is, but it's very easy to spoil your experiment.

Let's say you tell it that there might be small backdoors. You've now primed the LLM to search that way (even using "may"). You passed information about the test to test taker!

So we have a new variable! Is the success only due to the hint? How robust is that prompt? Does subtle wording dramatically change output? Does "may", "does", "can", "might" work but "May", "cann", or anything else fail? Have you the promoter unintentionally conveyed something important about the test?

I'm sure you can prompt engineer your way you greater success but by doing so you also greatly expand the complexity of the experiment and consequently make your results far less robust.

Experimental design is incredibly difficult due to all the subtleties. It's a thing most people frequently fail at (including scientists) and even more frequently fool themselves into believing stronger claims than the experiment can yield.

And before anyone says "but humans", yeah, same complexity applies. It's actually why human experimentation is harder than a lot of other things. There's just far more noise in the system.

But could you get success? Certainly. I mean you could tell it exactly where the backdoors are. But that's not useful. So now you got to decide where that line is and certainly others won't agree.