I asked the JTE beforehand about the students' ability to write. She was a bit skeptical but we both agreed to at least try if they could express themselves through writing while needing lesser help from us. Prior to this activity, we have already seen from a previous activity that students (at least in groups) could summarize and tell a story they just read in their own words.
Start with some warm up you prefer using the target grammar: I've been ~ing. We did a small talk about what we've been thinking about for summer vacation.
ALT then tells her own story about what she has been thinking about recently (or for a long time.)
Don't limit students from just writing about what they are thinking about. They can explore through different topics like: I've been admiring/collecting/playing/eating/watching/reading etc.
Ask the JTE to share her own story about what she's been into recently or for a long time. Write it on the board while she tells her story. By this, students could have a clear idea of what to do.
Walk around and try to read their stories, ask questions and show interest in it. They love it that the ALT appreciates what they've been into!
Give hints to students who have a hard time thinking of what next sentence they will write. For example, the student chose to talk about watching anime. You could give him a hint like talking about his fave anime, and what the story is about. With this, I saw that when I give hints of what sentence(s) they could write next, students tend to write in their own words without asking me how to write it in English.
Put students in groups and let them share their stories to the other members.