
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 the sum
\[
\sum_{n=1}^\infty \frac{b_n}{9^{n+1}}.
\]

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