I think Damian would originally be very reluctant to join but he is of course fuming with jealousy and he's like "I'm only joining so I can BEAT all these other kids because I'm a Desmond and I'm the BEST! I don't care about that Forger girl at all!" and everyone is like "sure Damian."
Becky sets up an elaborate quiz in which she makes the boys write poetry about Anya's eyes and quizzes them on appropriate flowers to gift and date ideas (note: she watches too many romance dramas) and Damian fails all of them because because he refuses to be sappy in front of everyone. Damian is internally panicking over the thought of losing Anya while simultaneously understanding his language skills suck and these other boys are better at wooing. All while in constant denial.
Becky was originally rooting for Damian but she gets frustrated because he's not even trying to be romantic. Meanwhile Anya is reading minds and is surprised by how most of her suitors genuinely admire her (vs girls only wanting Damian because of his family). And of course Damian's mind is a mess.
Damian slowly realises he is under-qualified but it's not like he cares, obviously he does not, he does not even remotely think about the Forger girl, he's just embarrassed he's going to get defeated, but it's not like dancing with a commoner is worth fighting for, right? Right?? Maybe he should just step away from this competition so instead of being defeated, it's framed as his choice to not dance with a commoner.
Anya starts panicking at the thought of Sy-on boy leaving (is it because of Plan B 👀 or is it because she wants to dance with him 👀) and hurriedly sets up a question that is worth ten points (so whoever answers correctly will win): what is Anya Forger's greatest secret?
Anya is staring straight at Damian and he's like ???????. Then he remembers she told him she could read minds... is that her greatest secret? But what's the point of asking if people know her secret if she wants to keep it a secret? Damian has enough awareness to not out Anya even if it's a joke. And if she can read minds, she would know he knows.
So Damian lies and says something impossible like "uhhhh Forger likes Bondman so her secret is that she's actually the child of a spy. Or something."
(Across the room, a waiter holding up a tray nearly drops it.)
Since no one can prove what Anya's secret is, Anya declares Damian is the winner (she is very biased) and pulls him away for world peace. And Damian can't even grumble about it after all of the effort he put in. The other boys accuse Damian of cheating. Becky complains that Damian doesn't know how to romance a girl.
As they dance, Damian thinks about Anya's odd final question and how it felt targeted towards him. He tells her he thinks her secret is that she wanted to dance with him as she would accept his answer no matter what it is. Anya is like :D because I want to go to your house! :D and they do the standard bickering.
Damian then calms down and asks why Anya didn't want to dance with the other boys even though they performed better in Becky's trials. Anya says she doesn't care about flowers and poetry. She then asks why he didn't answer with her actual secret that she told him.
Damian of course is like ???? it's a secret??? you DUMMY????? and starts rambling about how mind reading is a not a real thing, and if it is, Anya shouldn't tell anyone because it's dangerous, and it's totally not like he cares about her being in danger. Anya is touched by this and she can tell Damian won't tell anyone (even if he thinks it's a lie).
Now Anya realises Damian knows another secret about her: she truly wanted to dance with Damian. But why? Is it just for world peace? Or is it because it can only ever be him?