
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
Given the sequence $\{a_n\}$ with the general term $a_n=\log_{3} \frac{n}{n+1} (n\in\mathbb{N}^*)$, and let its sum of the first $n$ terms be $S_n$, then the smallest natural number $n$ that makes $S_n < -4$ true is $\boxed{\text{(C) } 81}$.

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