
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
Let points $A = (0, 0)$, $B = (2, 3)$, $C = (5, 4)$, and $D = (6, 1)$. A quadrilateral $ABCD$ is divided by a line passing through $A$, which bisects its area. This line intersects $\overline{CD}$ at a point $\left (\frac{p}{q}, \frac{r}{s} \right )$ in lowest terms. Find $p + q + r + s$.
A) 74  
B) 112  
C) 176  
D) 148  
E) 96

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