
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
Consider that $\frac{x}{x-k} = \frac{y^2 + 3y + 2}{y^2 + 3y + 1}$ where $k$ is a constant. Determine the value of $x$ in terms of $y$ and $k$.
A) \( ky^2 + 3ky + 3k \)  
B) \( ky^2 + 3ky + 2 \)  
C) \( ky^2 + 3ky + 2k \)  
D) \( ky^2 + 3ky - 2k \)

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