It's a sparsely populated town, and your companions are tiny, so there's no trouble at all leaving them all out.
The Depot Agent on the bridge is staring out over the train yard, occasionally tapping at a smart tablet, but not actually writing or doing much of anything. He's too distracted to notice you.
"Oh—!" He startles to attention. "For the Progressive Line? Wait, no... you mean the train that came here. Ahaha... Well, it shouldn't take too long. You can feel free to visit the town in the meantime! There may not be much in the way of tourist attractions, but you can see our control panel and visit our lost and found if you need it!"
This is a small, unassuming building. There aren't many items visible within it at a glance. There's a counter with a very cute plushie sitting on top. There's another Depot Agent sitting behind the counter, and he's comforting a young girl, who is on the customer side of the counter, crying.
She sniffles, shy, but appreciating Ritsuka leveling with her.
"It's white, and it has a brim, and some patches on it... And, my grandma gave it to me... I had it when I got off the train, but I don't know where it went after that..."
"I got off the train, and then I waited on the platform for a little while, and then I went onto the bridge and looked out at all the train tracks and the trains going to sleep... But then I realized after a while that—that it wasn't there anymore."
On the way back to the bridge you do pass a conspicuous control panel facing out over the train yard.
But you can make it back to the bridge without incident! You don't immediately see any hats on the bridge. The Depot Agent who is lost in thought is still there.
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The Depot Agent on the bridge is staring out over the train yard, occasionally tapping at a smart tablet, but not actually writing or doing much of anything. He's too distracted to notice you.
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[ She's cheerful about it at least, waving a little as she trots up. ]
Hey, sorry--do we have an estimate on how long the maintenance is gonna take?
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[ OFF TO THE LOST AND FOUND. She doesn't actually anticipate it being so easy to find anything significant there, but she has to at least try. ]
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[ Obviously not, but. You know. You gotta ask. ]
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The Depot Agent is clearly apologetic. "Sorry... We'll definitely be on the lookout."
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[ As she says that, she crouches down to be on eye level with the little girl. ]
Where did you last see it?
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"It's white, and it has a brim, and some patches on it... And, my grandma gave it to me... I had it when I got off the train, but I don't know where it went after that..."
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[ That is the sort of logic that usually works for little kids, okay. ]
Where did you go after you left the train? Maybe I can look. I'm planning on walking around a bit while I'm waiting.
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[ IT'S A FETCH QUEST BUT WHATEVER. THOSE USUALLY HAVE REWARDS. ]
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She gestures off from her head in a clumsy approximation of a bucket hat with a wide brim.
"And it has a Brycen-Man patch and a Charming Munna patch..."
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[ She gets to her feet again, ruffling the girl's hair. ]
I'll go take a look. You wait up for me, okay?
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The Depot Agent in here looks relieved at your assistance. "Th-Thank you so much!" he adds.
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[ TIME TO DOUBLE BACK TO THE BRIDGE since the little girl mentioned it. ]
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But you can make it back to the bridge without incident! You don't immediately see any hats on the bridge. The Depot Agent who is lost in thought is still there.