What is he thinking? Is there any shot of getting back with him?

So my boyfriend of almost 4 years and I broke up a little over a month ago. It started mutually as we were disagreeing a lot and he said he wanted space for us to both "work on ourselves". I almost immediately realized that I don't want this to end and I want to work things out together. I've never been more devastated in my life.

We live together. I'm not in a space where I can move out super easily and I am clinging on to hope that this will work itself out. We're sleeping in separate rooms but still share the same bathroom/his stuff is still in my room. I feel like I'm getting some mixed signals on what's happening here and what he's feeling. Like I mentioned, he has not moved any of this stuff out of our room other than his laptop. He goes out of his way to ask me how my day was and have conversations that feel like nothing even happened, just not with any of the romantic stuff, and he hangs around the same area as me if I'm cooking or something. We are constantly still doing things for each other like buying each other a drink/food when we're already getting something and doing favors.

He is not a very communicative person - that was one of our big issues. I get the vague feeling that he may still want me and I want him, but I'm way too nervous to say anything and I know he won't. Can someone help me get some clarity on what he might be thinking and if it's worth still holding on to hope? I want this to work but I can't be the only one putting in the work/chasing him anymore if there is no shot. What can I do to inch towards fixing this?

What is he thinking? Is there any shot of getting back with him?
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