<|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
 In a $6 \times 6$ toy board, each cell represents a light button. When someone presses a button, it lights up if it is off and turns off if it is on. Additionally, all buttons that share a side with the pressed button also change their state: from on to off or from off to on. Starting with all buttons off and pressing each button on the board exactly once, one at a time and in any order, how many buttons will be lit at the end? 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
20
In a $6 \times 6$ toy board, each cell represents a light button. When someone presses a button, it lights up if it is off and turns off if it is on. Additionally, all buttons that share a side with the pressed button also change their state: from on to off or from off to on. Starting with all buttons off and pressing each button on the board exactly once, one at a time and in any order, how many buttons will be lit at the end?
test