
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 $D = (6,1)$. Quadrilateral $ABCD$ is divided into equal area pieces by a line passing through point $A$. This line intersects segment $\overline{CD}$ at point $\left(\frac{p}{q}, \frac{r}{s}\right)$, where these fractions are in lowest terms. Determine $p + q + r + s.$
A) 15
   B) 18
   C) 20
   D) 22
   E) 24

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