
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 that the three vertices of triangle $\triangle ABC$ are $A(1,-1)$, $B(-1,3)$, $C(3,0)$, where $AD$ is the altitude from $A$ to $BC$ and $AE$ is the angle bisector of $\angle BAC$. Find:<br/>
$(1)$ The equation of line $AD$;<br/>
$(2)$ The equation of line $AE$.

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