
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
(1) Given the vertices of a triangle as A(2, 4), B(0, -2), and C(-2, 3), and M being the midpoint of segment AB, find the equation of the median line CM on side AB;  
(2) Given a circle with center E that passes through points P(0, -6) and Q(1, -5), and the center E is on the line l: x - y + 1 = 0, find the standard equation of the circle with center E.

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