
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
Let us consider a similar problem in which we have a right isosceles triangle instead of an equilateral triangle with hypotenuse 10 cm, which also forms the diameter of a circle. A minor segment is shaded between one end of the hypotenuse (vertex) and the midpoint of the hypotenuse on the circle. Calculate the area of this shaded region if the expression for the area in square centimeters is expressed as \( a\pi - b\sqrt{c} \).

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