
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
Determine the necessary conditions on $x$ and $y$ if $|x-\log_3 y|=x+\log_3 y$ where $x$ and $\log_3 y$ are real numbers.
A) $x = 0$
B) $y = 1$
C) $x = 0$ and $y = 1$
D) $x(y-1) = 0$
E) None of these

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