2. After finding two buttons, you need to press them in the correct order. The correct order is: press the button on the right first, and then press the button on the left.
If the order is correct, you will hear the organ open. At this point, the floor of the library center will rise, revealing a staircase leading to the basement.
After going down to the basement, you will find a mysterious door, which needs a key to open. The key can be found on the bookshelf in the basement.
After finding the key, use it to open the door and you can continue to explore.