
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 parabola \( y = x^2 \) intersects with the line \( y = 25 \). A circle is constructed on the segment between the points of intersection of the parabola and the line as its diameter. Find the area of the convex polygon whose vertices are the points of intersection of the given circle and the parabola. In your answer, indicate the nearest integer to this area.

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