
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 the sequence \(\left\{a_{n}\right\}\), which satisfies
\[ 
a_{1}=0,\left|a_{n+1}\right|=\left|a_{n}-2\right| 
\]

Let \(S\) be the sum of the first 2016 terms of the sequence \(\left\{a_{n}\right\}\). Determine the maximum value of \(S\).

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