
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
Given two positive numbers $x$ and $y$ that satisfy $x + y = 1$, find the minimum value of $z = (x + \frac{1}{x})(y + \frac{1}{y})$.

A) $\frac{33}{4}$
B) $\frac{25}{4}$
C) $\frac{1}{4}$
D) $\frac{\sqrt{17}}{4}$

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