
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 with equal heights are placed 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 $(8, 0)$. The rectangle has a width of $8$ units and a height of $12$ units, and the base of the triangle on the $x$-axis is $8$ 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?

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