
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 $a_1, a_2, \dots$ be a sequence defined by $a_1 = 2, a_2 = 3$ and $a_{n+2} = a_{n+1} + a_n$ for $n \geq 1$. Find
\[
\sum_{n=1}^\infty \frac{a_n}{3^{n+1}}.
\]

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