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Aquarina's mind was set, and she wanted to go on her own adventure with her friends. She didn't want them to see her as a kid anymore, and coming along with her for something that she considered a small adventure was ridiculous.
Although she acted a bit childish at the end, despite trying to prove she wasn't a child, her parents ended up agreeing with her and letting her go alone. Or well, not alone, but with her friends. Her mother was much against the idea though, anything related to the Gods could escalate into something incredibly dangerous.
Before, at the very least she was with Sylphy and all her other very strong friends, but right now she was on her own, with Silvia and Justicio, who might not be at the same level as the rest.
At the end, though, they decided to accept her deals, although her father handled her something, a ring.
"Take this at the very least, Aquarina."