In running my campaign I've noticed it's common for the group of players to discuss which among them should perform the dice check for the action they've decided to take.
I don't think this should necessarily happen every time (some players may be suggested by the group for the dice checks more often than others due to their stats , but I want everyone to be involved).
One encounter I had the player that came up with what to do make the dice check instead of having another group discussion about who should roll. Should I continue to encourage the player that comes up with an idea to make the dice check?
Also, another situation. Some players seem to be looking to me to provide them with their possible solutions to problems rather than using their imagination to come up with a possible solution on their own. I didn't notice until a player looked straight at me and asked what are their options.
I gave out vague suggestions but seeing as this was a conversation based encounter and they knew what information they needed, all that they would need to do is take a look at the skills listed on their character sheets. If they are completely stumped and it will stop the session from progressing I should obviously give them hints. However, should I maybe remind them that they can think of their own solutions to the problem at hand?