
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 the real number sequence \(a_{0}, a_{1}, \cdots\) satisfy \(a_{0} = 0\) and \(a_{1} = 1\). For each positive integer \(n \geqslant 2\), there exists a positive integer \(k\) (where \(1 \leqslant k \leqslant n\)) such that
\[
a_{n} = \frac{a_{n-1} + a_{n-2} + \cdots + a_{n-k}}{k}.
\]
Find the maximum value of \(a_{2018} - a_{2017}\).

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