
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 \( a_{0}, a_{1}, a_{2}, \ldots \) be a sequence of real numbers such that \( a_{0} = 0 \), \( a_{1} = 1 \), and for every \( n \geqslant 2 \) there exists \( 1 \leqslant k \leqslant n \) satisfying
\[ a_{n} = \frac{a_{n-1} + \cdots + a_{n-k}}{k} . \]

Find the maximal possible value of \( a_{2018} - a_{2017} \).

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