
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 $a \neq 1$ and $b \neq 1$ satisfy $\log_3{a} = \log_b{81}$ and $ab = 243$. What is $(\log_3{\tfrac{a}{b}})^2$?
A) 4
B) 9
C) 16
D) 25
E) 36

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