
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
How many sets $(a, b, c)$ of non-zero real numbers satisfy the equation
\[\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{a+b+c}\]
A) none  
B) 1  
C) 2  
D) infinitely many sets for each \(b \neq 0, c \neq 0\)  
E) two sets for each \(b \neq 0, c \neq 0\)

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