
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, there is an L-shaped region bounded by the horizontal and vertical segments with vertices at $(0,0), (0,4), (4,4), (4,2), (7,2)$, and $(7,0)$. Determine the slope of the line originating at the origin that bisects the area of this region.
A) $\frac{1}{2}$
B) $\frac{3}{5}$
C) $\frac{5}{8}$
D) $\frac{2}{3}$
E) $\frac{7}{10}$

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