
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 triangle $\triangle ABC$ has vertices at $A(1,1)$, $B(-1,3)$, and $C(3,4)$.
(1) Find the equation of the line $l_1$ which is the perpendicular height from point $B$ to side $AC$.
(2) If line $l_2$ passes through point $C$ and the distances from points $A$ and $B$ to line $l_2$ are equal, find the equation of line $l_2$.

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