
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
Positive integers  $x_1,...,x_m$  (not necessarily distinct) are written on a blackboard. It is known that each of the numbers  $F_1,...,F_{2018}$  can be represented as a sum of one or more of the numbers on the blackboard. What is the smallest possible value of  $m$ ?
(Here  $F_1,...,F_{2018}$  are the first  $2018$  Fibonacci numbers:  $F_1=F_2=1, F_{k+1}=F_k+F_{k-1}$  for  $k>1$ .)

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