
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
Positive real numbers $x \neq 1$ and $y \neq 1$ satisfy $\log_3{x} = \log_y{81}$ and $xy^2 = 243$. What is $(\log_3{\tfrac{x}{y}})^2$?
A) $\frac{1}{36}$
B) $\frac{16}{36}$
C) $\frac{49}{36}$
D) $\frac{64}{36}$

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