
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
In the Cartesian coordinate system, given that the coordinates of the three vertices of triangle ABC are $A(-3,0)$, $B(2,0)$, $C(0,-4)$, and a circle passing through these three points is denoted as $M$.
1. Find the general equation of the median line of side $BC$.
2. Find the equation of circle $M$.

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