
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
Suppose that \(x,\) \(y,\) and \(z\) are three positive numbers such that \(xyz = 1,\) \(x + \frac{1}{z} = 8,\) and \(y + \frac{1}{x} = 20.\) Find \(z + \frac{1}{y}.\)

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