
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 rectangular prism where the ratio of the shortest edge to the medium edge is equal to the ratio of the medium edge to the longest edge, which is also equal to the ratio of the longest edge to the face diagonal of the rectangle formed by the shortest and medium edge. What is the square of the ratio of the shortest edge to the medium edge of this prism?
A) $\frac{\sqrt{3}-1}{2}$
B) $\frac{1}{2}$
C) $\frac{\sqrt{5}-1}{2}$
D) $\frac{\sqrt{2}}{2}$
E) $\frac{\sqrt{6}-1}{2}$

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