
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 circle with a radius $r$ has a rectangle inscribed in it. The top and bottom sides of the rectangle are horizontal, and the bottom side of the rectangle lies on the horizontal diameter of the circle. If the height of the rectangle within the circle is $x$, determine the area of this rectangle.

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