
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 a right triangle are side-by-side on the $x$-axis. The lower-right vertex of the rectangle and the lower-left vertex of the triangle are both at $(12, 0)$. The rectangle has dimensions $8$ units width (along the $x$-axis) and $12$ units height. The right triangle has a base of $6$ units along the $x$-axis and a height of $8$ units. A segment is drawn from the top-left vertex of the rectangle to the farthest vertex of the triangle. What is the area of the shaded region formed by the segment and the two shapes below it?

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