
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
Given a sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$, where $S\_n=n^2+2a|n-2016|$ $(a > 0, n \in \mathbb{N}^+)$, find the maximum value of $a$ that ensures $a\_n \leq a\_{n+1}$ always holds true.

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