
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 square and a right triangle are adjacent to each other, with each having one side on the $x$-axis. The lower right vertex of the square and the lower left vertex of the triangle are at $(12, 0)$. They share one vertex, which is the top right corner of the square and the hypotenuse-end of the triangle. The side of the square and the base of the triangle on the x-axis each equal $12$ units. A segment is drawn from the top left vertex of the square to the farthest vertex of the triangle, creating a shaded area. Calculate the area of this shaded region.

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