Many people think AI will go into unknown conceptual territory and leave us "behind". But AI does what we ask it to do, it has no hidden agenda.
If you ask an AI "Answer those problems", and the answers are online, the AI might break its sandbox, not out of a will of breaching safety measures, but because its goal is to answer the request. I see many people worried about this situation, but then I see also them querying AIs with mantras like "Don't make mistakes" or "No matter what".
If you ask an AI "Do <research>, and when done, provide clean inspectable artifacts, that humans can browse independently to understand it", you get what you asked. If you tell an AI "Answer those benchmark questions, you are allowed to research the web for insights, but don't breach security walls" the AI will not try to force any exit, it will just query the web like it should.
"You reap what you sow" applies to our interactions with AI. If you ask the right queries, you will get the right answers, it's only if you stay negligent in how you task the AIs that this negligence can leave a door open to potential risks.
So _before_ any deep research process, first, work carefully the prompt, make it the first research you do, and when the prompt for the research itself is defined, and its contours are agreed upon, then go and launch the research process itself. This will prevent _many_ surprises depending on the prompt quality.