Forum:Which comes first - Priority or Respond?

I was wondering which comes first; the player declaring the use of his priority, OR asking the opponent if he would respond? I was in a local tournament when my opponent and I argued which would come first. As you see, it would really make a difference in this situation:

PlayerA summons Caius, the Shadow Monarch. Will he:

1. Declare his usage of priority and activate Caius's effect first 2. Or ask his opponent if his opponent would respond, before declaring his use of priority (Caius's effect)

If PlayerB has 300 life points and a set Torrential Tribute, the results from 1 and 2 will differ:

1. PlayerA (playing safe) will choose to remove the set T.Tribute if he would declare his use of priority first 2. PlayerA would just remove Caius if his opponent would respond first before declaring his use of priority, therefore winning the duel.

The situation above was almost the same as our situation that time. Please Help!