Opening the book…
A leader who never needs anything teaches everyone else that needing something is a weakness. Asking in public gives your team permission to ask, and it hands you information you were never going to get by being impressive. It also tests whether the trust you think you have built actually holds weight.
Pick something you genuinely cannot solve alone and put it in front of the group without a prepared answer hidden in your pocket. Say what you have tried and where you are stuck. Then take a suggestion you did not expect and actually use it, visibly, with credit.
Do not manufacture helplessness as a technique; a fake request is worse than none. And in an acute crisis where people need a decision now, lead first and ask for help once the room can breathe.