
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 $\{x_n\}$ satisfies $x_{n+1}=|x_n-x_{n-1}|(n\geqslant 2,n\in N)$, and $x_1=1$, $x_2=a(a\in R, a\neq 0)$, find the sum of the first 2016 terms of the sequence when the period of the sequence $\{x_n\}$ is the smallest.

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