
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
Let $x$, $y$, and $z$ be positive real numbers such that $\log_{2}x=\log_{3}y=\log_{5}z > 0$. Determine the possible relationship among $\frac{x}{2}$, $\frac{y}{3}$, and $\frac{z}{5}$.

A) $\frac{x}{2} < \frac{y}{3} < \frac{z}{5}$
B) $\frac{x}{2}= \frac{y}{3}=\frac{z}{5}$
C) $\frac{z}{5} < \frac{y}{3} < \frac{x}{2}$
D) $\frac{y}{3} < \frac{x}{2} < \frac{z}{5}$

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