
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 the expression \( (x+y+z)^{-1} \left(x^{-1}+y^{-1}+z^{-1}\right)(xy+yz+zx)^{-1}\left[(xy)^{-1}+(yz)^{-1}+(zx)^{-1}\right] \), simplify the value of the product of the given expression.

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