I think we win by taking 3 blue from the middle and placing them in row 3.
The only way for our opponent to force us to have the last move is by taking 3 blue right away (and put them in bottom row). But then we take 3 red (and place them in row 5). We end up with 4 stones in the discard pile and our opponent has 6 stones there.
If he takes 2 red or 1 red, we take the other red(s) and force our opponent to have the last move and discard 6 stones.
Final remark: I would find it easier if the initial problem statement did not say "Losing by 10, can you win this?" but "Trailing by 3 points, can you win this?". Since there have been several moves done in the 5th round, we are only behind 3 points (we have finished a column more, the two rows finished in round 5 give the same points to both players).