
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
The function $y=f(x)$ is an even function with the smallest positive period of $4$, and when $x \in [-2,0]$, $f(x)=2x+1$. If there exist $x\_1$, $x\_2$, $…x\_n$ satisfying $0 \leqslant x\_1 < x\_2 < … < x\_n$, and $|f(x\_1)-f(x\_2)|+|f(x\_2)-f(x\_1)|+…+|f(x\_{n-1}-f(x\_n))|=2016$, then the minimum value of $n+x\_n$ is \_\_\_\_\_\_.

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