Young Justice meets a Jinchuriki (Continued)

Training

This is a really really really short chapter because I need to think about how I want the mission to go, but I didn't want to go to long without updating.
Please give me ideas in the comments
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Naruto was ecstatic at the prospect of going on a "super special secret mission", but his family would never let him go unprepared. Naruto had to train with the Young Justice team after mastering his chakra control with Jiraiya.

Jiraiya was able to stay in town longer than expected so Naruto was able to thoroughly get a handle on his powers. He could transform into the Kyuubi, a miniature version though, and able to be in control if his body the whole time. Because of his large chakra reserves it took him a while to master tree climbing and walking on water, but he got it eventually.

Besides training with Jiraiya, Naruto was trained by Diana and other superheroes when they were free.

Batman taught him to be stealthy and how to hack all types of technology. Superman was the enforcer of "Superhero Morals". The Flash helped hone Naruto's reflexes and quicken his reaction time. Green lantern taught Naruto how, just like with Hal's ring, his chakra needed creativity to become more powerful. Wonder Woman was Naruto's spar partner. (She wouldn't let anyone else close to her baby)

Naruto's newfound skills were not only used in superhero training. In his Kyuubi form, Naruto was quite huggable and very comfortable to take a nap in. Naruto took advantage of this thoroughly by using this fact to get his way. Because of his relationship with the women of the Amazon, he was nicknamed the God of Cuddles.
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"Are you sure it's not too soon for him to go on real missions?" asked Diana worriedly.

"I understand what you're feeling, but he's shown us that he's ready. Even if things go wrong, he'll have the rest of the team to rely on," said Bruce comfortingly.

"I know, but still..." she trailed off

"If you want you can monitor the mission through the watchtower. You'll know everything that happens," he offered.

"Yeah, I'll do that," she said, a little calmer.

She had looked deep into this mission. It was important and a good way for Naruto to start in his superhero journey, but that didn't mean she didn't worry.
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Naruto could not be seen anywhere not wearing his jumpsuit. It would become his signature look soon if he wore it anymore. Even though the colors orange and blue often clash, Dick was able to design the outfit in a way so that didn't happen.

Even though the jumpsuit looked good and was durable, it wasn't proper superhero attire. (The Justice League had surprisingly strict regulations on what superheroes should wear) Because of this, the members of the bat-family had been working furiously to produce the best costume they could before the upcoming mission.

They done great amounts of research into the cultures of the Hidden Continent and of Diana's culture. They wanted it to tie to his roots and also show that Naruto was Wonder Woman's full fledged sidekick.

The costume design they settled on consisted of a traditional Kitsune mask, sword, kunai, black sleeves and legs, and red armor around the torso that was adorned with the Wonder Woman 'W'.

With training completed and proper superhero attire, Naruto was ready.
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Should I make them meet Naruto characters on the mission or should I keep it more DC?
What should Naruto's superhero name be?
Please answer in comments!!