
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 positioned side-by-side with their bases on the $x$-axis. The lower right vertex of the square and the lower left vertex of the triangle are each at $(15, 0)$. The side length of the square is $15$ units, and the base of the triangle is also $15$ units. The height of the right triangle is $15$ units. A segment is drawn from the top left vertex of the square to the right angle vertex of the triangle. Calculate the area of the shaded region that is formed by the segment within the triangle.

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