
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
Consider a diagram where a square and a right triangle share the same height, with both bases on the $x$-axis. The lower right vertex of the square and the lower left vertex of the triangle are at $(5, 0)$. The side of the square equals $5$ units, and the base of the triangle on the $x$-axis equals $10$ units. The triangle's other leg is also on the vertical line passing through $(15, 0)$. A segment is drawn from the top left vertex of the square to the farthest vertex of the triangle. What is the area of the shaded region within the triangle but outside the square?

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