
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
A line segment is divided into three parts, $x$, $y$, and $z$, such that, $x < y < z$ and $x$ to $y$ is as $y$ to $z$. If all three parts combined form a segment of length $s$, and $x + y = z$, determine the value of the ratio $\frac{x}{y}$.
A) $\frac{-1 - \sqrt{5}}{2}$
B) $\frac{-1 + \sqrt{5}}{2}$
C) $-\frac{1 + \sqrt{5}}{2}$
D) $\frac{1 - \sqrt{5}}{2}$

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