
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 $\{x_n\}$ satisfying $x_{n+2}=|x_{n+1}-x_{n}|$ for $n\in\mathbb{N}^*$, if $x_{1}=1$ and $x_{2}=a$ ($a\leqslant 1, a\neq 0$), and $x_{n+3}=x_{n}$ holds for any positive integer $n$, calculate the sum of the first 2016 terms of the sequence $\{x_n\}$.

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