Let $0 \le x \le 1.$  Find the maximum value of
\[x (1 - x)^5.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $0 \le x \le 1.$  Find the maximum value of
\[x (1 - x)^5.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{3125}{46656}
Let $0 \le x \le 1.$  Find the maximum value of
\[x (1 - x)^5.\]
train