
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, the coordinates of the vertices of triangle $\triangle ABC$ are $A(7,8)$, $B(10,4)$, $C(2,-4)$.
(1) Find the equation of the line containing the median from vertex $B$ to side $AC$.
(2) Find the equation of the line containing the altitude from vertex $B$ to side $AC$.

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