
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 share a common base on the x-axis. The lower left vertex of the rectangle and the right angle vertex of the triangle are at (8, 0). The rectangle has a base of 8 units and a height of 12 units, and the base of the triangle on the x-axis is also 8 units. A line segment is drawn from the top left vertex of the rectangle to the vertex of the triangle opposite the right angle. Calculate the area of the shaded region formed by this line segment within the triangle.

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