
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
In the $xy$-plane, an L-shaped region is defined by vertices at $(0,0), (0,4), (4,4), (4,2), (6,2)$, and $(6,0)$. Find the slope of the line through the origin that divides the area of this region exactly in half.
A) $\frac{1}{2}$
B) $1$
C) $1.5$
D) $2$
E) $2.5$

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