
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 that the sequence $\{3^{a_n}\}$ is a geometric sequence with the first term being $1$ and the common ratio being $3$, then the sum of the first $n$ terms of the sequence $\left\{ \frac{1}{a_{n+1}a_{n+3}} \right\}$, denoted as $S_n=$ ______.

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