
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 equations $\frac{xy}{x+y}= a, \ \frac{xz}{x+z}= b, \ \frac{yz}{y+z}= c$ and a constant $k$, where $a, b, c, k$ are non-zero constants, with a new condition that $\frac{xyz}{x+y+z} = k$, find the value of $x$.
**A)** $\frac{kbc}{ab+bc+ac}$  
**B)** $\frac{kab}{ab+bc+ac}$  
**C)** $\frac{2kab}{ab+bc-ac}$  
**D)** $\frac{2kab}{ab+bc+ac}$  
**E)** $\frac{2kab}{ab+bc-ac}$

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