
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
Solve for $x$ and $y$ given the equation $\frac{x+y}{x} = \frac{2y}{x+y}+1$ where $x \neq 0$ and $x + y \neq 0$.
A) $x = y \text{ and } x = 3y$  
B) $x = y \text{ or } x = 3y$  
C) $x = y \text{ or } x = -3y$  
D) $x = 2y \text{ or } x = -2y$  
E) $x = 2y \text{ and } x = -3y$

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