
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 any positive real numbers $a$, $b$, and $c$, compute the value of the product:
\[(a+b+c)^{-1}(a^{-1} + b^{-1} + c^{-1})(ab+bc+ac)[(ab)^{-1} + (bc)^{-1} + (ac)^{-1}]\]
**A)** $\frac{1}{a^2b^2c^2}$  
**B)** $\frac{(ab+bc+ac)^2}{abc}$  
**C)** $a+b+c$  
**D)** $\dfrac{1}{abc}$  
**E)** $\dfrac{1}{ab+bc+ac}$

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