
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
A line passing through point A = (1,1), point B = (2,4), point C = (5,4), and point D = (6,1) divides quadrilateral ABCD into two equal area pieces. This line intersects segment CD at point (p/q, r/s), where these fractions are in simplest form. Determine the value of p + q + r + s.

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