
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 = (2,1), C = (5,4), and D = (6,0). A quadrilateral ABCD is divided into two 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. Determine p+q+r+s.

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