
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
Let $b_1 = 2, b_2 = 3$, and define the remainder of the sequence by $b_{n+2}=b_{n+1}+b_n$ for $n \geq 1$. Find the sum
\[
S = \sum_{n=1}^\infty \frac{b_n}{3^{n+2}}.
\]

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