
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
If $x$, $y$, and $z$ are positive numbers satisfying:
\[
x+\frac{1}{y}=5,\ \ \ y+\frac{1}{z}=2, \ \text{and}\ z+\frac{1}{x}=\frac{8}{3},
\]
find the value of $xyz$.

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