
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
If $\frac{x}{x-2} = \frac{y^2 + 3y + 1}{y^2 + 3y - 1},$ then $x$ equals
A) $2y^2 + 6y + 1$  
B) $2y^2 + 6y + 2$  
C) $y^2 + 3y + 1$  
D) $y^2 + 3y - 1$  
E) $2y^2 + 6y - 1$

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