
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 the three vertices of $\triangle ABC$ are $A(0,1)$, $B(0,-1)$, $C(-2,1)$.
(1) Find the equation of the line $l$ containing the altitude on edge $BC$;
(2) Find the equation of the midline of edge $AC$;
(3) Find the equation of the circumcircle of $\triangle ABC$.

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