
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 $\triangle ABC$ are $A(1,1)$, $B(-1,3)$, and $C(3,4)$.

(1) Find the equation of the line $l_{1}$ on which the altitude of side $BC$ lies;

(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}
user