
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 right triangle, the ratio of the shorter leg to the longer leg is the same as the ratio of the longer leg to the hypotenuse. Find the square of the ratio of the shorter leg to the longer leg.
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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