
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
The point $S$ is the intersection of the lines $l_{1}: 7x + 5y + 8 = 0$ and $l_{2}: 3x + 4y - 13 = 0$. On the line $PQ$ formed by the points $P(3, 7)$ and $Q(11, 13)$, there are two points $A$ and $B$. Point $P$ lies between points $A$ and $Q$, and point $B$ lies between points $P$ and $Q$. Additionally, $\frac{|PA|}{|AQ|} = \frac{|PB|}{|BQ|} = \frac{2}{3}$. Without finding the coordinates of $S$, determine the equations of the lines $SA$ and $SB$.

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