
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 even function $y=f(x)$ satisfies $f(x+3)=f(3-x)$, and $f(x)=2^{-x}$ when $x\in[-3,0]$. If there exist $x_1, x_2, \ldots, x_n$ such that $0\leq x_1 < x_2 < \ldots < x_n$, and $|f(x_1)-f(x_2)|+|f(x_2)-f(x_3)|+\ldots+|f(x_{n-1})-f(x_n)|=2019$, then the minimum value of $x$ is $\_\_\_\_\_\_$.

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