
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
In a circle with center $O$, the diameter $MN$ is drawn. Point $K$ is the midpoint of the arc $MN$, point $E$ is the midpoint of the chord $MK$, and point $B$ is the midpoint of the arc $KN$. The chord $AB$, which passes through point $E$, is drawn. A rectangle $ABCD$ is constructed such that $AB$ is one side of the rectangle and vertices $C$ and $D$ also lie on the circumference of the circle. Find the area of the rectangle $ABCD$ if the diameter of the circle is $d$.

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