<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 On an \(8 \times 8\) chessboard, 6 black rooks and \(k\) white rooks are placed on different cells so that each rook only attacks rooks of the opposite color. Compute the maximum possible value of \(k\). (Two rooks attack each other if they are in the same row or column and no rooks are between them.) Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
14
On an \(8 \times 8\) chessboard, 6 black rooks and \(k\) white rooks are placed on different cells so that each rook only attacks rooks of the opposite color. Compute the maximum possible value of \(k\). (Two rooks attack each other if they are in the same row or column and no rooks are between them.)
test