
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 $x_1, x_2, \ldots, x_n$ satisfying $0 \leq x_1 < x_2 < \ldots < x_n$, and $|f(x_1) - f(x_2)| + |f(x_2) - f(x_3)| + \ldots + |f(x_{n-1}) - f(x_n)| = 2016$, then the minimum value of $n + x_n$ is $\boxed{1513}$.

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