
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 \(x \neq 0\) or \(2\) and \(y \neq 0\) or \(3\), then determine the values \(x\) and \(y\) for which \(\frac{3}{x} + \frac{2}{y} = \frac{5}{6}\).
A) \(x = \frac{18y}{5y - 12}\)  
B) \(x = \frac{12y}{5y - 18}\)  
C) \(x = \frac{5y}{18y - 12}\)  
D) \(x = \frac{6y}{18y - 5}\)  
E) None of these

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