If you are able to excuse yourself from them and retreat to your own private room that is probably the easiest way out. There you can chat with others that don't ostracize you for not following the party line. And also watching tv-series on Hulu or Netflix or just plain dl'ing them is a good way to kill time.
Then to avoid them thinking you are a nut, or make them wonder even more, you can "play a game" with them where you stage your private room a different way each day when you leave, so if they look they will just be confused.
One example could be…. hard to think of any that won't make them think you are a bit crazy, but plenty of ideas on how to mess with their minds. Or rather it is more expensive to stage a room that messes with their mind and also makes you look sane. Decorating the room in a different national theme costs more than laying out individual socks or underwear all over the room. Both can be fun but the latter could give them the wrong idea. But since it is only ten months I say go the cheep route where you lay out different garments each day. Or you can make a "scene" like "flanellograf" out of the clothes depicting mundane stuff, or someone trying to climb up on the bed, or whatever comes to mind that day.>pic related (but perhaps bad example if you want to make them less suspicious)
If they report you all you have to do is tell the authorities is that you do it for shits and giggles, and to get the time to pass. And that you are political right and they are hard core leftists that don't tolerate different opinions so you choose to keep to yourself rather than creating conflict. They will understand that you are no threat and move on forgetting about you.