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Space Jump up and through the secret passage in the ceiling, and into the goo. Then, Space Jump out of the left side of it. Move left from there to the first wall. Not the wall farthest to the left, but the smaller one at the base of it. Look at the example below to see the exact location that you must stand at.

While standing still, Space Jump straight up, until that wall is out of veiw. Then stop your jump and fall back down to where you jumped from. As soon as you let yourself fall, do the the Select Trick. When you land (back to where you jumped from), there should be an opening in the wall in front of you. (2)

If not, then give it another try; it may take several. But when there is a hole, go through it. After you pass that hole, let yourself fall. (3) You'll land in a large checkered area. (4) You've made it!

From here, you're on your own! But, I'll show you some places where you can go and things that you can do.

A neat thing about this world is that you can save your progress in it! To do this, start from where you first land in that checkered area and run all the way to the left. From there, go right a little bit and jump up. (The reason you go right before you jump up is so that you don't get stuck in a wall above.) (5)

Land yourself on (but not in) the ledge in the screen above, and move left again. You'll fall; let yourself fall a few screens. You'll land in another checkered area, but this time, go right. When the screen stops scrolling, keep moving right. You'll run into an area with junk scattered all over the place. But among this junk, is also a lot of different save points. Pick one, and save your progress! Now, you're free to explore!
By the way, try not to get stuck; it's easy.