
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 $b_1, b_2, \dots$ be a sequence defined by $b_1 = 2$, $b_2 = 3$, and $b_{n+2} = b_{n+1} + b_n$ for $n \geq 1$. Find \[
\sum_{n=1}^\infty \frac{b_n}{3^{n+1}}.
\]

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