
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 parallelogram $ABCD$ with the coordinates of three vertices as $A(-1,4)$, $B(-2,-1)$, and $C(2,3)$.

$(1)$ Find the equation of the line on which side $AD$ lies;

$(2)$ In $\triangle ACD$, find the equation of the line on which the altitude from $C$ to side $CD$ lies.

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