
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 \( A = (0,0), B = (0,3), C = (4,4), \) and \( D = (5,0) \). Quadrilateral \( ABCD \) is cut into equal area pieces by a line passing through \( A \). This line intersects \( \overline{CD} \) at point \( \left( \frac{p}{q}, \frac{r}{s} \right) \), where these fractions are in lowest terms. Find \( p + q + r + s \).
A) 12
B) 13
C) 14
D) 15
E) 16

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