There's a brief stare at the hand - though brief. It's not even because she's debating whether or not to shake it in the first place, or anything like that. It's just Ange thinking about those words he said right before it.

Yes, that sounds like Martin, alright.

She takes his hand, giving it a brief shake, her gaze at the same time rising to meet his own.

"I'm Ange. Ange Ushiromiya."

She decides to shove aside the weirdness of the idea that she's introducing herself to someone she knows so well, and instead tries to see it as a new start. Trying everything all over again.

"And.. I guess we should go into the lighthouse now, right? It kind of feels inevitable." Like it's still pulling on them.