
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
We call functions of the form $$y= \frac {b}{|x|-a} \ (a＞0，b＞0)$$ "Jiong functions" because their graphs resemble the Chinese character "囧". The point symmetric to the intersection point of the "Jiong function" and the y-axis with respect to the origin is called the "Jiong point". Any circle that has common points with the "Jiong function" with the "Jiong point" as its center is called a "Jiong circle". When $a=1$ and $b=1$, the minimum area among all "Jiong circles" is \_\_\_\_\_\_.

Present the answer in LaTex format: \boxed{Your answer}
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