
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 vertex $B(-1,-3)$, the equation of the line containing the altitude $CE$ from $AB$ is $4x+3y-7=0$, and the equation of the line containing the median $AD$ from $BC$ is $x-3y-3=0$.  
$(1)$ Find the equation of line $AB$;  
$(2)$ Find the coordinates of point $C$.

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