
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 a triangle $\triangle ABC$ with vertices $A(3,0)$, $B(4,5)$, and $C(0,7)$:  
(1) Find the equation of the line that represents the height from vertex $A$ to side $BC$ (Please express the solution in the general form of a line equation).  
(2) Find the equation of the line that represents the median from vertex $A$ to side $BC$ (Please express the solution in the general form of a line equation).

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