
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
For all positive numbers $x$, $y$, $z$, the product 
\[
(2x+2y+2z)^{-1}(x^{-1}+y^{-1}+z^{-1})(xy+yz+xz)^{-1}[2(xy)^{-1}+2(yz)^{-1}+2(xz)^{-1}]
\]
A) $\frac{1}{2xyz}$
B) $\frac{1}{xyz}$
C) $\frac{1}{x^2y^2z^2}$
D) $\frac{1}{2x^2y^2z^2}$

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