
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 $A$ divides quadrilateral $ABCD$ into equal area pieces. Find the coordinates of the point of intersection with $\overline{CD}$.

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