
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 $\triangle ABC$ with $A(1, -4)$, $B(6, 6)$, and $C(-2, 0)$. Find:  
(1) The equation in general form and intercept form of the line where the median parallel to side $BC$ in $\triangle ABC$ lies;  
(2) The equation in general form of the median line on side $BC$, and convert it into intercept form.

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