
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_0,a_1,a_2,\dots $  be a sequence of real numbers such that  $a_0=0, a_1=1,$  and for every  $n\geq 2$  there exists  $1 \leq k \leq n$  satisfying \[ a_n=\frac{a_{n-1}+\dots + a_{n-k}}{k}. \]Find the maximum possible value of  $a_{2018}-a_{2017}$ .

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