
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
Given that $l\_1$ and $l\_2$ are two perpendicular lines on a plane, their intersection point is $A$, and two moving points $B$ and $C$ (distinct from point $A$) are on $l\_1$ and $l\_2$ respectively, with $BC=3$, calculate the area of the circle passing through points $A$, $B$, and $C$.

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