
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 side-by-side, with both bases on the x-axis. The lower right vertex of the rectangle and the lower left vertex of the triangle are at (12, 0). The base of the rectangle on the x-axis is 12 units and its height is 8 units, while the base of the triangle is 12 units. A segment is drawn from the top left vertex of the rectangle to the farthest vertex of the triangle. Calculate the area of the shaded region formed by the intersection of the segment and the triangle.

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