
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
A rectangle and an isosceles triangle of equal height are positioned side-by-side along the $x$-axis. The bottom right vertex of the rectangle and the bottom left vertex of the triangle are both located at $(12, 0)$. The rectangle extends 12 units along the $x$-axis, and the triangle stretches 8 units along the $x$-axis. Both the rectangle and the triangle have the same height of 10 units. A line segment is drawn from the top left vertex of the rectangle to the farthest vertex of the triangle. Determine the area of the shaded region which forms between the line segment and the bases of the rectangle and the triangle.

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