
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 numbers \( a_{1}, a_{2}, \cdots, a_{2011} \) satisfy
\[ 
\begin{aligned}
a_{1} &= a_{2017}, \\
\left|a_{i}+a_{i+2}-2 a_{i+1}\right| &\leq 1 \quad (i=1,2, \cdots, 2015).
\end{aligned}
\]
Let \( M = \max_{1 \leq i < j \leq 17} \left| a_{i} - a_{j} \right| \). Find the maximum value of \( M \).

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