
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 the three vertices of triangle ABC are A(-4, 0), B(0, 2), and C(2, -2), find:
1. The equation of the line containing the altitude drawn from point A to side BC;
2. The equation of the circumcircle of triangle ABC.

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