On 05/05 you'll be able to accept request from the Fox in the Shrine. Every fulfilled request will increase your rank in the Hermit Arcana Social Link by 1 point. Accepting a request will not consume time, however reporting after your completed request will do. You can accept and report any day, even the rainy ones.
I want things to go well with the person I like! Edit
Will enable Quest 06: I Wish for Love