
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  $(a_n)$  be defined by  $a_1=a_2=1$  and  $a_n=a_{n-1}+a_{n-2}$  for  $n>2$ . Compute the sum  $\frac{a_1}2+\frac{a_2}{2^2}+\frac{a_3}{2^3}+\ldots$ .


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