
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
We call  $\overline{a_n\ldots a_2}$  the Fibonacci representation of a positive integer  $k$  if \[k = \sum_{i=2}^n a_i F_i,\] where  $a_i\in\{0,1\}$  for all  $i$ ,  $a_n=1$ , and  $F_i$  denotes the  $i^{\text{th}}$  Fibonacci number ( $F_0=0$ ,  $F_1=1$ , and  $F_i=F_{i-1}+F_{i-2}$  for all  $i\ge2$ ). This representation is said to be  $\textit{minimal}$  if it has fewer 1’s than any other Fibonacci representation of  $k$ . Find the smallest positive integer that has eight ones in its minimal Fibonacci representation. 

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