
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 \( x_{1}, \ldots, x_{m} \) (not necessarily distinct) are written on a blackboard. It is known that each of the numbers \( F_{1}, \ldots, F_{2018} \) 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 \( F_{1}, \ldots, F_{2018} \) 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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