
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
Consider the polygon in the $xy$-plane with vertices at $(0,0)$, $(0,4)$, $(4,4)$, $(4,2)$, $(6,2)$, $(6,0)$. Determine the slope of the line through the origin that divides the area of this region exactly in half.
A) $\frac{1}{2}$
B) $\frac{2}{3}$
C) $\frac{3}{2}$
D) $\frac{5}{3}$
E) $\frac{7}{4}$

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