<|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
 What is the minimum number of colors required to paint all the cells of a 6 by 6 square grid such that each row, column, and diagonal of the square has all cells with different colors? Note: A diagonal of the square is defined as all rows of at least two cells going diagonally from one edge of the square to the other at an angle of $45^\circ$ or $135^\circ$ to the horizontal. 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
7
What is the minimum number of colors required to paint all the cells of a 6 by 6 square grid such that each row, column, and diagonal of the square has all cells with different colors? Note: A diagonal of the square is defined as all rows of at least two cells going diagonally from one edge of the square to the other at an angle of $45^\circ$ or $135^\circ$ to the horizontal.
test