
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 placed side by side with their bases on the $x$-axis. The lower left vertex of the square and the lower right vertex of the triangle are both located at $(12, 0)$. The side of the square is 12 units and the base of the triangle on the $x$-axis is also 12 units. The height of the triangle is 9 units. A segment is drawn from the top left vertex of the square to the hypotenuse of the triangle. Calculate the area of the shaded region formed.

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