
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
Three congruent circles with centers $X$, $Y$, and $Z$ are tangent to the sides of rectangle $EFGH$. The circle centered at $Y$ has a diameter of $6$ and passes through points $X$ and $Z$. Calculate the area and the perimeter of the rectangle $EFGH$.
A) Area: 72, Perimeter: 34
B) Area: 72, Perimeter: 36
C) Area: 78, Perimeter: 36
D) Area: 64, Perimeter: 38

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