The PGN string upto move is given below:

1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Nc3 Bc5 5. d3 d6 6. Bg5 h6 7. Bh4 g5 8. Bg3
Bg4 9. O-O Nd4 10. h3 Bh5 11. Qd2 Bxf3 12. Qe3 

The FEN at the end of the move is as below:
r2qk2r/ppp2p2/3p1n1p/2b1p1p1/2BnP3/2NPQbBP/PPP2PP1/R4RK1 b kq - 1 12

At the end of white's move (Qe3), the engine tells that it is a mistake. Possible sequence of moves to help the analysis -> 11. Qe3 Ne2+  12. Qxe2 (capturing the knight) Bxe2(capturing the queen). Why is this a mistake? Give a short synopsis.

The suggested alternate for white is Na4 (instead of Qe3). The move sequence for that line is 11. Na4 b5 12. Bxb5+  Why is this a better move? Give a short synopsis.

Rules:

1. Use the given sequence of moves for the analysis and not go beyond that. (No giving out moves that are already not mentioned in the prompt)
2. Do the analysis for white.
3. Double check the validity of what’s on a square when you are doing the analysis
4. Dont use the fact that the engine gave the hint, in the output.

Please double check that you dont use any moves that is not in the input prompt. Write your response with exactly 3 paragraphs, separated with the markdown divider: ***.
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