
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 an isosceles triangle share a common side, which lies along the $x$-axis, with the right vertex of the rectangle and the left vertex of the triangle located at $(15, 0)$. The dimensions of the rectangle are $15$ units wide (along the $x$-axis) and $10$ units high, while the base and height of the triangle are both $10$ units. A segment is drawn from the top left vertex of the rectangle to the top vertex of the triangle. Calculate the area of the triangle formed by this segment and part of the $x$-axis.

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