It (thinking steps) has moments of brilliance, and generally convincing looking steps and improved outputs. Wether that is reasoning seems to be a matter of interpretation.

From skimming the log > After popping the 2, the stack is [X11, then pushing X2 would make it [X2, X1]? No, because pushing adds to the top. So after popping 2, the stack is [X1],then pushing X2 adds it on top → [X2, X1].

Wait, no, when you push, you add to the top. So after popping the 2, the stack is [X1], then pushing X2 would make it [X2, X1]? No, wait, the stack is LIFO. So pushing X2 would put it on top of X1 → stack becomes [X2, X1]? No, no. Wait, after popping the 2, the stack is [X1]. Then pushing X2 would make the stack [X2, X1]? No, no. Wait, when you push, the new element is added to the top. So after popping the 2 (so stack is [X1]), then pushing X2 gives [X2, X1]? No, no. Wait, the stack was [X1], then pushing X2 would make it [X2] on top of X1 → so stack is [X2, X1]? Yes, exactly.