
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 points $A = (0,0)$, $B = (2,3)$, $C = (4,4)$, and $D = (5,0)$. A line passing through $A$ cuts quadrilateral $ABCD$ into two pieces of equal area. This line intersects $\overline{CD}$ at point $\left (\frac{p}{q}, \frac{r}{s} \right )$, where these fractions are in their lowest terms. Determine the sum $p + q + r + s$.

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