
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 \(a_{1}, a_{2}, \ldots\) be a sequence defined by \(a_{1}=a_{2}=1\) and \(a_{n+2}=a_{n+1}+a_{n}\) for \(n \geq 1\). Find
\[
\sum_{n=1}^{\infty} \frac{a_{n}}{4^{n+1}} .
\]

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