
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 three real numbers \( x, y, z \) that satisfy the system of equations
\[
\begin{cases}
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 2, \\
\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = 1,
\end{cases}
\]
calculate the value of \( \frac{1}{xy} + \frac{1}{yz} + \frac{1}{zx} \).

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