Find the number of ordered pairs $(x,y)$ of real numbers that satisfy
\[x^2 + 2y^2 + \frac{1}{2} \le x(2y + 1).\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the number of ordered pairs $(x,y)$ of real numbers that satisfy
\[x^2 + 2y^2 + \frac{1}{2} \le x(2y + 1).\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
Find the number of ordered pairs $(x,y)$ of real numbers that satisfy
\[x^2 + 2y^2 + \frac{1}{2} \le x(2y + 1).\]
train