
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
The angles of a triangle are \( \boldsymbol{A} \), \( \boldsymbol{B} \), and \( C \). The height of the triangle passing through the vertex of angle \( B \) is given. On this height, a circle is constructed such that the height is its diameter. The points where the circle intersects the sides \( \boldsymbol{AB} \) and \( \boldsymbol{BC} \) of the triangle are connected to the ends of the height. Find the area of the constructed quadrilateral.



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