
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, consider the T-shaped region bounded by horizontal and vertical segments with vertices at $(0,0), (0,5), (2,5), (2,2), (7,2)$ and $(7,0)$. Determine the slope of the line through the origin that divides the area of this region exactly in half.

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