
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, given that the vertices of the rhombus $ABCD$ are $A(0,2)$ and $C(4,6)$, and the equation of the line containing $AB$ is $3x-y+2=0$.  
$(1)$ Find the general equation of the line containing the diagonal $BD$.  
$(2)$ Find the general equation of the line containing $AD$.

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