
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
Consider a rectangle $EFGH$, where a circle with radius $s$ is tangent to side $EF$, side $EH$, and side $GH$. The circle also passes through the midpoint of diagonal $EG$. Determine the area of rectangle $EFGH$ in terms of $s$.
A) $s^2$  
B) $2s^2$  
C) $4s^2$  
D) $6s^2$  
E) $8s^2$

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