
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
The graph of the function in the form \( y=\frac{b}{|x|-a} \) (where \( a, b > 0 \)) resembles the Chinese character "唄". It is referred to as the "唄 function", and the point symmetric to its intersection with the y-axis about the origin is called the "目 point". A circle with its center at the 明 point that intersects the 唄 function is called the "唄 circle". For \( a=b=1 \), the minimum area of all 唄 circles is .

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