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Like the flavortext says, you have to solve the top portion of the puzzle before you can use the diary entries at the bottom. Of the three columns, one corresponds to water, one to earth, and one to fire.
The left column corresponds to water and is a word puzzle. Think about what might lexicographically fall within the given ranges, and what might go in the ? to complete the set. The ?s are all related to water in some way.
The middle column corresponds to earth. The actual comic series at webcomicname.com isn't relevant, but its name indicates that this subpuzzle is about Spider-Man. When you've identified which Spider-Man each panel refers to, the speech bubbles will let you extract.
The right column corresponds to fire. When you've identified each song, try figuring out what their titles have to do with each other.
|water, earth, fire||
Solving the top portion of the puzzle produces a series of words in the left column, a series of digits in the middle column, and an ordering in the right column. Reorder by the right column, keeping each row together, then index into the words, to discover how to interpret the diary entries.
|air, diary, freedom||
Each diary entry clues both an episode of Avatar: The Last Airbender and a freedom of the air. All of these are unique. The entries are given alphabetically.
Index the freedom number into the episode title and reorder chronologically.
Before he can complete his journey to save the world, Aang needs to master the elements of water, earth, and fire in order to discover what he values most.
Hi diary! It’s been a while, I guess. Now, what order did these all happen in?
- I wonder what Appa’s been up to... I bet he’s escaping from an evil circus! And meeting a wise guru at a temple! And coming back to Ba Sing Se...
- Uuugh. We stopped here in the Fire Nation just for a bit to rest and refill our supplies, but I can’t sleep. I just keep worrying!
- I stopped the attack on the North Pole! Now we’re heading from there to the Earth Kingdom. I hope they’ll be nice to us: I’m the Avatar, after all.
- Sokka told me how his dad got flown to that Fire Nation jail from the capital as a prisoner of war. I’m sorry, buddy, that’s rough.
- Man, those tank things didn’t seem so fast the first time we saw them at the temple. But now every time we touch down, it’s just a few hours behind us...
- Sokka doesn’t seem that impressed by the giant canyon. Maybe we’ll just keep flying over it instead of stopping...
- My new friends Sokka and Katara are leaving home for the first time, so I’m taking them to the closest temple. They’re gonna love it!
- Azula attacked us! With airships?! I think she blew up the whole temple... guess we’re back to hiding out in the Fire Nation.
- We headed out from the temple to the last bit of Earth Kingdom land so we could set off across the ocean from there. And now we’re at the North Pole! We finally made it!