
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 a region made of a rectangle and an isosceles triangle on top. The rectangle has vertices at $(0,0), (0,2), (4,2), (4,0)$, and the triangle has its base along the top side of the rectangle extending from $(1,2)$ to $(3,2)$ with the third vertex at $(2,4)$. Find the slope of the line through the origin that divides the area of this region exactly in half.
A) $1$
B) $1.5$
C) $2$
D) $2.5$
E) $3$

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