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That they meet is pure accident due to Casey taking a smoking break outside, and Jin is outside walking and thinking in himself.
Jin's father is a scholar in architecture, while Casey recently finished her study in architecture, and often giving tours through the city for interested guests.
It looks like staff finds excuses on behalf of her mom why she cannot answer the phone or why she cannot meet.
There was one example where Jin and Casey were outside the clinic, discussing the architecture of the clinic as exemplary transparent (plenty of glass), allowing them to see one of the nurses answering the phone but apparently acting differently from what she promised to do.
Visitors are invited to partake in the conservatory’s education, cultural, and social events or to simply walk around and appreciate the exceptional plant collection, garden, seasonal art, and nature-based exhibitions that the conservatory hosts.
So I have to recommend everyone to read the synopsis beforehand.
The situations of the two main protagonists has many similarities that binds them together after a random encounter while taking a smoking break outside, though it takes some time before they really open up to one another and clarify their respective situations towards another (and implicitly to oneself, as a side effect).
It is one example where the architectural tour through the city coincides with their domestic issues.
Precisely this common dilemma brings Casey and Jin together.