
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 \[\sum_{n=1}^\infty \dfrac{a_n}{4^{n+1}}.\]

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