In the complex plane, let $S$ be the set of complex numbers $z$ such that
\[\left| z + \frac{1}{z} \right| \le 2.\]Find the area of $S.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In the complex plane, let $S$ be the set of complex numbers $z$ such that
\[\left| z + \frac{1}{z} \right| \le 2.\]Find the area of $S.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2 \pi + 4
In the complex plane, let $S$ be the set of complex numbers $z$ such that
\[\left| z + \frac{1}{z} \right| \le 2.\]Find the area of $S.$
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