
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 the coordinates of three fixed points of $\triangle ABC$ are $A(0,1)$, $B(0,-1)$, and $C(-2,1)$.
1. Find the equation of the line $l$ that is the altitude from vertex $B$ to side $BC$.
2. Find the equation of the median from vertex $A$ to side $AC$.
3. Find the equation of the circumcircle of $\triangle ABC$.

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