
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 all \(n \geq 2\), there exists \(1 \leq k \leq n\) such that

\[ 
a_n = \frac{a_{n-1} + \cdots + a_{n-k}}{k} 
\]

What is the maximum value of \(a_{2018} - a_{2017}\)?

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